Simultaneous Solution Research Articles

FlexibleSUSY 2.0: Extensions to investigate the phenomenology of SUSY and non-SUSY models

We document major new features and improvements of FlexibleSUSY, a Mathematica and C++ package with a dependency on the external package SARAH, that generates fast and precise spectrum generators. The extensions presented here significantly increase the generality and capabilities of the FlexibleSUSY package, which already works with a wide class of models, while maintaining an elegant structure and easy to use interfaces. The FlexibleBSM extension makes it possible to also create spectrum generators for non-supersymmetric extensions of the Standard Model. The FlexibleCPV extension adds the option of complex parameters to the spectrum generators, allowing the study of many interesting models with new sources of CP violation. FlexibleMW computes the decay of the muon for the generated model and thereby allows FlexibleSUSY to predict the mass of the W boson from the input parameters by using the more precise electroweak input of {GF,MZ,αem} instead of {MW,MZ,αem}. The FlexibleAMU extension provides a calculator of the anomalous magnetic moment of the muon in any model FlexibleSUSY can generate a spectrum for. FlexibleSAS introduces a new solver for the boundary value problem which makes use of semi-analytic expressions for dimensionful parameters to find solutions in models where the classic two-scale solver will not work such as the constrained E6SSM. FlexibleEFTHiggs is a hybrid calculation of the Higgs mass which combines the virtues of both effective field theory calculations and fixed-order calculations. All of these extensions are included in FlexibleSUSY 2.0, which is released simultaneously with this manual. Program summaryProgram title:FlexibleSUSYProgram Files doi:http://dx.doi.org/10.17632/kf7m8gn8vp.1Licensing provisions: GPLv3Programming language: C++, Wolfram/Mathematica, FORTRAN, Bourne shellJournal reference of previous version: Comput.Phys.Commun. 190 (2015) 139–172Does the new version supersede the previous version?: YesReasons for the new version: Program extension including new models, observables and algorithmsSummary of revisions: Extension to non-supersymmetric models (FlexibleBSM), complex parameters (FlexibleCPV), prediction of W boson mass from muon decay (FlexibleMW), calculation of anomalous magnetic moment of the muon (FlexibleAMU), semi-analytic boundary value problem solver (FlexibleSAS), improved hybrid Higgs mass calculation (FlexibleEFTHiggs).Nature of problem: Determining the mass spectrum, mixings and further observables for an arbitrary extension of the Standard Model, input by the user. The generated code must find simultaneous solutions to constraints that are specified at two or more different renormalization scales, which are connected by renormalization group equations forming a large set of coupled first-order differential equations.Solution method: Nested iterative algorithm and numerical minimization of the Higgs potential.Restrictions: The couplings must remain perturbative at all scales between the highest and lowest boundary condition. Tensor-like Lagrangian parameters of rank 3 are currently not supported. The automatic determination of the Standard Model-like gauge and Yukawa couplings is only supported for models that have the Standard Model gauge group SU(3)C×SU(2)L×U(1)Y as a gauge symmetry group factor. However, due to the modular nature of the generated code, adapting and extending it to overcome restrictions in scope is quite straightforward.

Nonlinear interaction of an intense radio wave with ionospheric D/E layer plasma

This paper considers the nonlinear interaction of an intense electromagnetic wave with the D/E layer plasma in the ionosphere. A simultaneous solution of the electromagnetic wave equation and the equations describing the kinetics of D/E layer plasma is obtained; the phenomenon of ohmic heating of electrons by the electric field of the wave causes enhanced collision frequency and ionization of neutral species. Electron temperature dependent recombination of electrons with ions, electron attachment to O2 molecules, and detachment of electrons from O2− ions has also been taken into account. The dependence of the plasma parameters on the square of the electric vector of the wave E02 has been evaluated for three ionospheric heights (viz., 90, 100, and 110 km) corresponding to the mid-latitude mid-day ionosphere and discussed; these results are used to investigate the horizontal propagation of an intense radio wave at these heights.

Biohydrogen Production from Pineapple Waste: Effect of Substrate Concentration and Acid Pretreatment

Biohydrogen is the ultimate choice of energy carrier in future due to its superior qualities such as fewer greenhouse gases emission, high energy density (142 kJ/gram), and high energy conversion using a fuel cell. Production of biohydrogen from organic waste e.g. pineapple waste offers a simultaneous solution for renewable energy production and waste management. It is estimated that pineapple cultivation in Indonesia generated more than 1 million ton/year comprising of rotten pineapple fruit, leaves, and stems. Majority of this waste is dumped into landfill area without any treatments which lead to many environmental problems. This research was meant to investigate the utilization of pineapple waste i.e. peel and the core of pineapple fruit and leaves to produce biohydrogen through mesophilic dark fermentation (30°C, 1 atm, pH 5.0). Effect of dilute acid treatment and substrate concentration was particularly investigated in these experiments. Peel and core of pineapple waste were subjected to fermentation at 3 various substrate concentration i.e. 8.8, 17.6 and 26.4-gram VS/liter. Meanwhile, pineapple leaves were pretreated using dilute acid (H2SO4) at 0.2, 0.3 and 0.4 N and followed by dark fermentation. Results show that the highest yield of biohydrogen was obtained at a substrate concentration of 26.4-gram VS/liter both for peel and core of the waste. Pretreatment using dilute acid (H2SO4) 0.3 N might improve fermentation process with a higher yield at 0.8 ml/gram VS. Hydrogen percentage in biogas produced during fermentation process was in the range between 5 – 32% of volume ratio. In summary, it is possible to utilize pineapple waste for production of biohydrogen at an optimum substrate concentration of 26.4-gram VS/liter and acid pretreatment (H2SO4) of 0.3 N.

A film-based integrated chip for gene amplification and electrochemical detection of pathogens causing foodborne illnesses

Given the increased interest in public hygiene due to outbreaks of food poisoning, increased emphasis has been placed on developing novel monitoring systems for point-of-care testing (POCT) to evaluate pathogens causing foodborne illnesses. Here, we demonstrate a pathogen evaluation system utilizing simple film-based microfluidics, featuring simultaneous gene amplification, solution mixing, and electrochemical detection. To minimize and integrate the various functionalities into a single chip, patterned polyimide and polyester films were mainly used on a polycarbonate housing chip, allowing simple fabrication and alignment, in contrast to conventional polymerase chain reaction, which requires a complex biosensing system at a bench-top scale. The individual integrated sensing chip could be manually fabricated in 10 min. Using the developed film-based integrated biosensing chip, the genes from the pathogens causing foodborne illnesses were simultaneously amplified based on multiple designed microfluidic chambers and Hoechst 33258, which intercalates into double-stranded DNA, to generate the electrochemical signal. The target pathogen gene was accurately analyzed by square wave voltammetry (SWV) within the 25 s, while the gel electrophoresis required about 30 min. Based on the developed integrated biosensing chip, the 1.0 × 101 and 1.0 × 102 colony-forming unit (CFU) of Staphylococcus aureus and Escherichia coli were sensitively detected with high reproducibility in the 25 s. On the basis of the significant features of the film-based molecular analysis platform, we expect that the developed sensor could be applied to the screening of various pathogens as a POCT device.

Integrated order picking and vehicle routing with due dates

Supermarkets typically order their goods from a centrally located distribution center (warehouse). Each order that the warehouse receives is characterized by the requested items, the location of the respective supermarket and a due date by which the items have to be delivered. For processing an order, a human operator (order picker) retrieves the requested items from their storage locations in the warehouse first. The items are then available for shipment and loaded on the vehicle which performs the tour including the respective location of the supermarket. Whether and to which extent a due date is violated (tardiness) depends on the composition of the tours, the corresponding routes and the start dates of the tours (vehicle routing subproblem). The start date of a tour, however, is also affected by the assignment of orders to pickers and the sequence according to which the orders are processed by the pickers (order picking subproblem). Although both subproblems are closely interconnected, they have not been considered simultaneously in the literature so far. In this paper, an iterated local search algorithm is designed for the simultaneous solution of the subproblems. By means of extensive numerical experiments, it is shown that the proposed approach is able to generate high-quality solutions even for large instances. Furthermore, the economic benefits of an integrated solution are investigated. Problem classes are identified, where the sequential solution of the subproblems leads to acceptable results, and it is pointed out in which cases an integrated solution is inevitable.

Stochastic porous media modeling and high-resolution schemes for numerical simulation of subsurface immiscible fluid flow transport

This paper proposes stochastic petroleum porous media modeling for immiscible fluid flow simulation using Dykstra–Parson coefficient (VDP) and autocorrelation lengths to generate 2D stochastic permeability values which were also used to generate porosity fields through a linear interpolation technique based on Carman–Kozeny equation. The proposed method of permeability field generation in this study was compared to turning bands method (TBM) and uniform sampling randomization method (USRM). On the other hand, many studies have also reported that, upstream mobility weighting schemes, commonly used in conventional numerical reservoir simulators do not accurately capture immiscible displacement shocks and discontinuities through stochastically generated porous media. This can be attributed to high level of numerical smearing in first-order schemes, oftentimes misinterpreted as subsurface geological features. Therefore, this work employs high-resolution schemes of SUPERBEE flux limiter, weighted essentially non-oscillatory scheme (WENO), and monotone upstream-centered schemes for conservation laws (MUSCL) to accurately capture immiscible fluid flow transport in stochastic porous media. The high-order schemes results match well with Buckley Leverett (BL) analytical solution without any non-oscillatory solutions. The governing fluid flow equations were solved numerically using simultaneous solution (SS) technique, sequential solution (SEQ) technique and iterative implicit pressure and explicit saturation (IMPES) technique which produce acceptable numerical stability and convergence rate. A comparative and numerical examples study of flow transport through the proposed method, TBM and USRM permeability fields revealed detailed subsurface instabilities with their corresponding ultimate recovery factors. Also, the impact of autocorrelation lengths on immiscible fluid flow transport were analyzed and quantified. A finite number of lines used in the TBM resulted into visual artifact banding phenomenon unlike the proposed method and USRM. In all, the proposed permeability and porosity fields generation coupled with the numerical simulator developed will aid in developing efficient mobility control schemes to improve on poor volumetric sweep efficiency in porous media.

A semi-analytical approach for analysis of the transient linear flow regime in tight reservoirs under three-phase flow conditions

The majority of current techniques for production data analysis of hydraulically-fractured horizontal wells only consider single- or two-phase flow conditions. Three-phase flow is expected to occur in many practical scenarios of low-permeability reservoir production when water (frac fluid and/or formation) production is occurring along with hydrocarbon phases. In this paper, a new semi-analytical method is developed to allow production data analysis of wells producing from low-permeability (tight) reservoirs exhibiting three-phase during the transient linear flow period.The proposed technique is based on the modified black oil formulation and is developed by employing the Boltzmann transformation. The modified black oil formulation comprises three highly nonlinear Partial Differential Equations (PDE's) that describe the flow of water, oil and gas in the reservoir. The use of the Boltzmann transformation allows conversion of this set of governing fluid flow PDE's to a set of Ordinary Differential Equations (ODE's) that can be easily solved using numerical techniques such as the Runge-Kutta method. In this paper, oil relative permeability under three-phase flow conditions is modelled using Stone's well-known first model.A theoretical basis for the occurrence of straight lines on a plot of 1/q vs √t for any producing phase is provided herein. The slope of the line is a function of the flowing fluid properties, and the reservoir and fracture characteristics. One important advantage of using the Boltzmann transformation is that the linear flow parameter, xf√k, can be directly estimated as a part of the solution process without the need for defining any complex pseudo-variable transformations. The results demonstrate that the relative error in xf√k estimation is generally less than 10% for different fluid models and relative permeability curves. Moreover, the simultaneous solutions of the ODE's provide the pressure and phase saturations as unique functions of the Boltzmann variable; these can be used to find relationships between pressure and phase saturations that in turn can be utilized for other rate transient analysis applications. The derived pressure-saturation relationships are in excellent agreement with numerical simulation for different three-phase relative permeability models.The significance of this paper is that a new theoretical and practical framework is introduced for the first time to analyze three-phase production data for transient linear flow under constant flowing bottomhole pressure conditions. These conditions are of practical importance for many tight production scenarios where water, in addition to hydrocarbon phases, are mobile in the reservoir. The results are validated using numerical simulation.

Quantitative analysis of a conceptual system dynamics maintenance performance model using multi-objective optimisation

This paper presents a quantitative analysis of a conceptual, system dynamics (SD) model by the application of multi-objective optimisation (MOO). The SD model investigates the strategic development of maintenance performance, using a system view of maintenance costs, while the execution of MOO evaluates multiple simulation runs, seeking the simultaneous trade-off solutions of the three conflicting objectives: maximise availability, minimise maintenance costs, and minimise maintenance consequential costs. The study explores three scenarios that represent companies at different states of developed maintenance performance. The application of this integrated, simulation-based optimisation approach reveals multiple analyses of system behaviour of the SD model, which are presented in a compact format to a decision-maker. Actually, notwithstanding the application to a conceptual model, the study results make explicit the nonlinearity between invested maintenance cost and its consequent effects. Furthermore, the approach demonstrates the contribution to the process of strengthening the usefulness of the conceptual maintenance performance model.

Attitude Correction Using Corner Landmarks in 3-D SLAM

This paper discusses the use of three-dimensional (3-D) corner features extracted from a 2-D laser scanner as landmarks in a simultaneous localization and mapping solution. The corner landmarks can be identified and tracked using their angles, and the observations of the corners are directly used to correct attitude errors. The proposed method can be used to navigate a small unmanned aerial vehicle in urban and indoor environments.

Convergence and complexity study of GMRES variants for solving multi-frequency elastic wave propagation problems

In this paper we present a comparison study of three different frameworks of iterative Krylov methods that we have recently developed for the simultaneous numerical solution of frequency-domain wave propagation problems when multiple wave frequencies are present. The three approaches have in common that they require the application of a single shift-and-invert preconditioner at a suitable seed frequency. In particular for three-dimensional problems, we present the efficient application of the elastic shift-and-invert preconditioner by means of an additive coarse grid correction. The focus of the present work lies, however, on the performance of the respective iterative method. We conclude with numerical examples that provide guidance concerning the suitability of the three methods.

Testing the Distance Scale of the Gaia TGAS Catalogue by the Kinematic Method

We have studied the simultaneous and separate solutions of the basic kinematic equations obtained using the stellar velocities calculated on the basis of data from the Gaia TGAS and RAVE5 catalogues. By comparing the values of Omega_0' found by separately analyzing only the line-of-sight velocities of stars and only their proper motions, we have determined the distance scale correction factor p to be close to unity, 0.97+/-0.04. Based on the proper motions of stars from the Gaia TGAS catalogue with relative trigonometric parallax errors less than 10% (they are at a mean distance of 226 pc), we have found the components of the group velocity vector for the sample stars relative to the Sun (U,V,W)o=(9.28,20.35,7.36)+/-(0.05,0.07,0.05) km s^{-1}, the angular velocity of Galactic rotation Omega0=27.24+/-0.30 km s^{-1} kpc^{-1}, and its first derivative Omega_0'=-3.77+/-0.06 km s^{-1} kpc^{-2}; here, the circular rotation velocity of the Sun around the Galactic center is V_0=218+/-6 km s^{-1} kpc (for the adopted distance R_0=8.0+/-0.2 kpc), while the Oort constants are A=15.07+/-0.25 km s^{-1} kpc^{-1} and B=-12.17+/-0.39 km s^{-1} kpc^{-1}, p=0.98+/-0.08. The kinematics of Gaia TGAS stars with parallax errors more than 10% has been studied by invoking the distances from a paper by Astraatmadja and Bailer-Jones that were corrected for the Lutz-Kelker bias. We show that the second derivative of the angular velocity of Galactic rotation Omega_0"=0.864+/-0.021 km s^{-1} kpc^{-3} is well determined from stars at a mean distance of 537 pc. On the whole, we have found that the distances of stars from the Gaia TGAS catalogue calculated using their trigonometric parallaxes do not require any additional correction factor.

Randomized Truncated SVD Levenberg‐Marquardt Approach to Geothermal Natural State and History Matching

AbstractThe Levenberg‐Marquardt (LM) method is commonly used for inverting models used to describe geothermal, groundwater, or oil and gas reservoirs. In previous studies, LM parameter updates have been made tractable for highly parameterized inverse problems with large data sets by applying matrix factorization methods or iterative linear solvers to approximately solve the update equations. Some studies have shown that basing model updates on the truncated singular value decomposition (TSVD) of a dimensionless sensitivity matrix achieved using Lanczos iteration can speed up the inversion of reservoir models. Lanczos iterations only require the sensitivity matrix times a vector and its transpose times a vector, which are found efficiently using adjoint and direct simulations without the expense of forming a large sensitivity matrix. Nevertheless, Lanczos iteration has the drawback of being a serial process, requiring a separate adjoint solve and direct solve every Lanczos iteration. Randomized methods, developed for low‐rank matrix approximation of large matrices, are more efficient alternatives to the standard Lanczos method. Here we develop LM variants which use randomized methods to find a TSVD of a dimensionless sensitivity matrix when updating parameters. The randomized approach offers improved efficiency by enabling simultaneous solution of all adjoint and direct problems for a parameter update.

Demographic growth, Harrodian (in)stability and the supermultiplier

A basic Kaleckian model is enriched by three simple, intuitive assumptions. First, there is a redistributive system of the wage bill between employed and unemployed workers, the latter receiving subsistence income. Second, only individuals with an income above the subsistence level build savings. The combination of these two assumptions gives rise to an autonomous consumption component whose rate of growth depends on population growth. Consequently, the rate of capital accumulation spontaneously converges towards the rate of population growth (the supermultiplier effect), a dynamic that offers a solution to one of the two Harrodian instability problems. The third assumption corresponds to entrepreneurs’ attempts to adjust investments to restore the normal rate of capacity utilisation. Although this assumption usually generates knife-edge instability, we show here that the stabilising properties of the supermultiplier, provided that the accelerator effect is not overly strong, help overcome this instability and realise the normal rate of capacity utilisation. Therefore, the model may offer a simple, simultaneous solution to the two Harrodian instability problems.

A simultaneous spectroscopic and photometric study of two eclipsing binaries: V566 Oph and V972 Her

In this study, we have performed simultaneous solutions of light and radial velocity curves of two eclipsing binary systems, V566 Oph and V972 Her. We observed both systems spectroscopically with a very recently installed spectrograph on the 40 cm telescope, T40, located in Ankara University Kreiken Observatory (AUKR), for the first time. We made use of the photometric data from the Hipparcos satellite for V972 Her, while we obtained the photometric observations of V566 Oph by using the 35 cm telescope, T35, located also in our observatory campus. We derived the absolute parameters for both systems and discussed their evolutionary states. In addition to the simultaneous analysis, we have also analyzed the change in mid-eclipse times for V566 Oph, and found cyclic variations, for which we have discussed light-time effect and magnetic activity as their potential origin, superimposed on a secular change due to a mass transfer between the components of the binary.

Genetic algorithm for multi-parameter estimation in sorption and phase equilibria problems

ABSTRACTThe techniques of applying single and multi-objective optimization (MOO) for single/multiple parameters estimation in sorption and phase equilibria calculations were demonstrated, and it was shown that non-dominated sorting genetic algorithm with jumping genes adaptation is a useful tool for standard nonlinear regressions. Simultaneous description of vapor liquid equilibrium (VLE) and the heat of mixing (excess enthalpy) are considered a complex task in applied thermodynamics. MOO problem for simultaneous VLE and excess enthalpy prediction was formulated by (1) transforming multi-objectives into an aggregated/single scalar objective function, and (2) formulating independent objectives and solving simultaneously. It was shown that GA leads to an entire set of equally good optimal solutions known as Pareto-optimal fronts. However, simultaneous solution of MOO problem produced a wide range Pareto-optimal solution than that of the weighted sum approach. Pareto-optimal solutions are important process knowledge from which a decision-maker can opt for any set based on the applications/requirements.

Block algorithms of a simultaneous difference solution of d’Alembert's and Maxwell's equations

The work is devoted to the synthesis of block algorithms of the FDTD method. In particular, the simultaneous difference solution of d’Alembert's and Maxwell's equations is considered. Accounting for the computer memory hierarchical structure allows the calculation time to be reduced up to six times when compared with the known software implementations of the method.

Тенденции развития совмещенных магнито-электроиндукционных электромеханических преобразователей энергии

The modern state of the electromechanical science is reviewed. State of the art in combined inductive-capacitive electromechanics is considered, and the fields of its possible practical applications and prospects for its further development are analyzed. A new approach for mathematical description of transients in dually conjugated dynamic systems is proposed, and the differential equations for combined inductive-capacitive electromechanical energy converters are derived proceeding from the proposed approach. The generalized Lagrangian theory of combined inductive-capacitive electric machines is developed as uniting the generalized Lagrangian models of inductive and capacitive electro-mechanical energy converters developed proceeding from the fundamental principles of binary-conjugate electrophysics. The possibility of optimizing an inductive generator’s operating mode using a capacitive generator with setting up a parallel or a series resonant circuit (with the interaction matrix serving as the controlling parameter) has been determined. The combined device is essentially a resonant machine, which has the best power performance indicators. The electrodynamic and electromechanical equations of combined inductive-capacitive electrical machines are given for the case when the structure of their excitation system contains ferroelectromagnets serving as dual-purpose active electrotechnical materials. The necessary Lagrangian for combined inductive-capacitive energy converters has been constructed by introducing a new matrix describing the interaction (mutual influence) between the inductive and capacitive subsystems. Simultaneous solution of these equations fully determines the dynamic behavior and power performance characteristics of the generalized model of combined machines of different designs and in any modes of interaction between their functional elements. It is shown that combined inductive-capacitive electromechanical converters have great prospects for use in microsystem electromechanics (for example, in microdrives at the level of nanotechnologies).

NATIONAL AND SOCIAL СOMPONENTS OF UKRAINIAN REVOLUTION 1917–1921 IN N. HRYHORYIV'S VISION

The paper considers the national and social aspects of the Ukrainian revolution of 1917–1921 in the conception of the national-state construction by N. Hryhoryiv. Public figure and politician Nykyfor Hryhoryiv was one of the active participants and theorists of the Ukrainian Revolution of 1917–1921, the Minister of Education of the Ukrainian People's Republic, a member of the Central Rada, one of the leaders of the Ukrainian party of Socialist-Revolutionaries. He created the original conception of national-state construction in Ukraine of that period, which is relevant today.
 According to him, the Ukrainian national revolution of 1917–1921 had a pronounced social color, and simultaneous solution of national and social issues became its main task and distinctive feature. He considered the achievement of Ukraine’s national sovereignty as the goal of the Ukrainian nationalliberation movement in the national-political sphere. At the same time, as a socialist-revolutionary, one of the theorists of ethical socialism, he stressed the necessity of a social revolution and construction of the Ukrainian state on the principles of «labor democracy».
 Based on these principles and the political situation in 1917, N. Hryhoryiv advocated a democratic federal republic and wide autonomy of Ukraine – its full sovereignty in internal affairs. Subsequently, when the situation changed, instead of autonomy, he demanded full independence of Ukraine from Russia.
 According to his opinion, the social character of the Ukrainian state was to be realized through a political system in the form of the so-called labor democracy, which corresponded to his principle of social and political freedom of the Ukrainian people. His concept gives each citizen not only the right to vote in elections, but also gives him the tools of constant and direct influence on the solution of all issues – from production to general political. 
 The national and social components of N. Hryhoryiv’s conception are not only closely linked but mutually complement each other in the creation of the Ukrainian state. In his opinion, only in such a way the Ukrainians could fully create a strong independent state and a successful society.

Efficient simultaneous solution of multi-physics multi-scale nonlinear coupled system in HTR reactor based on nonlinear elimination method

Pebble bed HTR reactor core is a globally coupled system involving neutronics and thermal-hydraulic field. At the same time, the locally coupled relations exist in fuel sphere temperature, local neutron flux and pebble bed temperature. What’s more, several types of fuel spheres with different burnup and fission power must be treated separately. Due to the essential difference between local and global coupling properties, the method, named nonlinear elimination (NlEm), is developed in this paper to solve the multi-physics/multi-scale system of HTR in a tightly coupled, two-level nonlinear form. In the NlEm framework, the local coupled variables and the global coupled variables are treated separately at two different levels to enhance the computational efficiency. For comparison, the Jacobian-free Newton Krylov (JFNK) method and the Picard method are utilized to solve the multi-physics/multi-scale system respectively. The numerical results reveal that the computational efficiency of NlEm is 6.7 times higher than that of Picard method and 3.5 times higher than that of JFNK method for five transient cases of a two-dimension simplified reactor model. And with the increase of the computational scale and time step size, the speedup ratio of NlEm is further raised.

Gradually varied flow profile based on adaptive pattern

The basic equation of gradually varied flow (GVF) describes gradual changes in its water surface elevation. One of the challenges of numerical integration is determining the appropriate integration spatial step size. In this study, the water surface elevations in GVF are calculated by adaptive Runge–Kutta method and adaptive Newton–Raphson method. The steps are calculated using error estimation during calculation, this procedure is smart and increases accuracy and speed of computation of the water surface profiles in GVF. In order to show the efficiency and accuracy of these methods, the results of these two methods are compared with each other and the results obtained through direct Step method in several applications. The differences between the results are negligibly small. Finally, as practical applications the proposed methods are applied to study changes of water surface profile due to channel bed aggradation in GVF and cyclic looped network. Obtained results show 56% reduction in the CPU time compared with previous method (Simultaneous solution method).