Method Of Undetermined Coefficients Research Articles

A MODEL OF INFLATION TRANSMISSION IN AN EXCHANGE RATE TARGET ZONE

I incorporate an exchange rate target zone with intramarginal interventions in a small open economy model. Using the method of undetermined coefficients, I solve for the price level and the nominal exchange rate to determine how price shocks from the large economy affect the small open economy. The results show that the behaviour of inflation transmission within the band differs from the behavior of inflation transmission at the edge of the band of the target zone. Foreign shocks can affect local prices in both cases but the central bank can respond through market interventions within the band while it cannot do so at the edge. Near the edge of the band, a central bank has to intervene to stop the exchange rate from breaching the band. My model predicts that if the interventions are robust, then the exchange rate is mean reverting and an exchange rate target zone can insulate an economy from foreign price shocks. Based on the model, central bank interventions contribute to long-run price stability in a target zone regime. Finally, I empirically test the model using unit root and cointegration tests, and present some policy implications.

Comparing method of undetermined coefficients with modification rule and method of variation of parameters

In this research article we have used the method of undetermined coefficients with modification rule and method of variation of parameters to solve linear ordinary differential equations and found that the method of variation of parameters is the easiest method to use.

Comparing method of undetermined coefficients with modification rule and method of variation of parameters

In this research article we have used the method of undetermined coefficients with modification rule and method of variation of parameters to solve linear ordinary differential equations and found that the method of variation of parameters is the easiest method to use.

A high accuracy scheme of three layers and nine points for Solving the concentration diffusion equation

A three layers and nine points implicit difference scheme is proposed for solving the one dimensional diffusion equation, using the method of undetermined coefficients and the accuracy is . Though the numerical solution and the Von Neumann analysis, the stability condition is proved to be . The stability condition and accuracy of the scheme are verified by numerical calculation. Compared with the existing three—layers scheme, this paper’s scheme reaches a higher accuracy in case of less nodes. In summary, the scheme mentioned in this paper has academic significance and application value.

The method of particular solutions using trigonometric basis functions

In this paper, the method of particular solutions (MPS) using trigonometric functions as the basis functions is proposed to solve two-dimensional elliptic partial differential equations. The inhomogeneous term of the governing equation is approximated by Fourier series and the closed-form particular solutions of trigonometric functions are derived using the method of undetermined coefficients. Once the particular solutions for the trigonometric basis functions are derived, the standard MPS can be applied for solving partial differential equations. In comparing with the use of radial basis functions and polynomials in the MPS, our proposed approach provides another simple approach to effectively solving two-dimensional elliptic partial differential equations. Five numerical examples are provided in this paper to validate the merits of the proposed meshless method.

Comments on “Shilnikov chaos and Hopf bifurcation in three-dimensional differential system”

In the commented paper, the authors consider a three-dimensional system and analyze the presence of Shilnikov chaos as well as a Hopf bifurcation. On the one hand, they state that the existence of a chaotic attractor is verified via the homoclinic Shilnikov theorem. The homoclinic orbit of this system is determined by using the undetermined coefficient method, introduced by Zhou et al. in [Chen's attractor exists, Int. J. Bifurcation Chaos 14 (2004) 3167–3178], a paper that presents very serious shortcomings. However, it has been cited dozens of times and its erroneous method has been copied in lots of papers, including the commented paper where an even expression for the first component of the homoclinic connection is used. It is evident that this even expression cannot represent the first component of a Shilnikov homoclinic connection, an orbit which is necessarily non-symmetric. Consequently, the results stated in Section 3, the core of the paper, are worthless. On the other hand, the study of the Hopf bifurcation presented in Section 4 is also wrong because the first Lyapunov coefficient provided by the authors is incorrect.

Classification of voltage sag disturbance sources using fuzzy comprehensive evaluation method

The classification and recognition of voltage sag disturbance sources is the foundation of mitigating voltage sags. This study analysed characteristics of various kinds of voltage sags, including sags caused by short-circuit faults, energising of transformers and starting of large induction motors. According to the features of different sources, an evaluation index set was formed by three-phase voltage unbalance factor, duration ratio and increments of second harmonic. After that, the weight of each element was calculated by analytic hierarchy process. A novel kind of estimation criterion for fuzzy membership function parameters was proposed, inspired from 95% probability value, based on the method of undetermined coefficient to establish the functions. Consequently, according to it, fuzzy membership functions were created for each index. Further, comprehensive index membership degrees were calculated to judge the disturbance source according to the maximum of the degrees. The presented estimation criterion can efficiently reduce the influence of sample errors and thus improve the accuracy of the whole process, which was verified with the use of data obtained from both simulations and measurements.

A new Mittag-Leffler function undetermined coefficient method and its applications to fractional homogeneous partial differential equations

A new Mittag-Leffler function undetermined coefficient method and its applications to fractional homogeneous partial differential equations

Cubic–quartic optical solitons in Kerr and power law media

In this paper, we present the exact bright and singular optical solitons of the nonlinear Schrödinger equation with third and fourth order dispersion terms. The method of undetermined coefficients is applied to obtain the reported solutions. The cases of Kerr law and power law nonlinearity are taken into account. We also find the conditions concerning the optical material parameters for the existence of these soliton structures. The results are useful in describing the propagation of optical solitons in highly dispersive media with Kerr and power law nonlinearity.

Optical solitons for Lakshmanan–Porsezian–Daniel model with spatio-temporal dispersion using the method of undetermined coefficients

This paper obtains optical soliton solutions to the Lakshmanan–Porsezian–Daniel model. The method of undetermined coefficients is applied to extract these solutions. Bright, dark and singular soliton solutions are obtained and the constraint conditions for the existence of these solitons are presented.

Solving Monetary (MIU) models with Linearized Euler Equations: Method of Undetermined Coefficients

This paper attempts to solve a benchmark money in utility model by first order Taylor approximation to the policy function. After a brief summary of recent development in first order Taylor approximation in solving dynamic stochastic general equilibrium models, we choose Sidrauski’s Money in utility model as a standard model and follow the approach proposed by Uhlig [1] to solve for the recursive law of motion at first order.

Stochastic elastic equation driven by multiplicative multi-parameter fractional noise

In this paper, we consider the stochastic elastic equation driven by multiplicative multiparameter fractional noise. By using the Wiener chaos expansion and undetermined coefficient methods, we obtain the existence and uniqueness of the solution in a distribution space. The asymptotic behavior and the Hölder index of the solution are also estimated.

High-order scheme for the source-sink term in a one-dimensional water temperature model.

The source-sink term in water temperature models represents the net heat absorbed or released by a water system. This term is very important because it accounts for solar radiation that can significantly affect water temperature, especially in lakes. However, existing numerical methods for discretizing the source-sink term are very simplistic, causing significant deviations between simulation results and measured data. To address this problem, we present a numerical method specific to the source-sink term. A vertical one-dimensional heat conduction equation was chosen to describe water temperature changes. A two-step operator-splitting method was adopted as the numerical solution. In the first step, using the undetermined coefficient method, a high-order scheme was adopted for discretizing the source-sink term. In the second step, the diffusion term was discretized using the Crank-Nicolson scheme. The effectiveness and capability of the numerical method was assessed by performing numerical tests. Then, the proposed numerical method was applied to a simulation of Guozheng Lake (located in central China). The modeling results were in an excellent agreement with measured data.

Justification of Wold’s Theorem and the Unbiasedness of a Stable Vector Autoregressive Time Series Model Forecasts

In this work, the multivariate analogue to the univariate Wold’s theorem for a purely non-deterministic stable vector time series process was presented and justified using the method of undetermined coefficients. By this method, a finite vector autoregressive process of order [] was represented as an infinite vector moving average () process which was found to be the same as the Wold’s representation. Thus, obtaining the properties of a process is equivalent to obtaining the properties of an infinite process. The proof of the unbiasedness of forecasts followed immediately based on the fact that a stable VAR process can be represented as an infinite VEMA process.

System Reduction and Finite-Order VAR Solution Methods for Linear Rational Expectations Models

This paper considers the solution of a large class of linear rational expectations (LRE) models and its characterization via finite-order VARs. The solution of the canonical LRE model can be cast in state-space form and solved for by the method of undetermined coefficients. In this paper I propose a novel approach that simplifies the characterization of the solution into finite-order VAR form and checks its existence and uniqueness based on the solution of a Sylvester equation. Solving LRE models with a finite-order VAR representation by this method is straightforward to implement, efficient, and can be handled easily with standard matrix algebra. An application to the workhorse New Keynesian model with accompanying Matlab codes is provided to illustrate the practical implementation of the procedure.

Qualitative analysis and approximate damped oscillatory solutions for a kind of nonlinear dispersive-dissipative equation

This paper makes qualitative analysis to the bounded traveling wave solutions for a kind of nonlinear dispersive-dissipative equation, and considers its solving problem. The relation is investigated between behavior of its solution and the dissipation coefficient. Further, all approximate damped oscillatory solutions when dissipation coefficient is small are presented by utilizing the method of undetermined coefficients according to the theory of rotated vector field in planar dynamical systems. Finally, error estimate is given by establishing the integral equation which reflects the relation between approximate and exact damped oscillatory solutions applying the idea of homogenization principle.

Combining Long Division of Polynomials and Exponential Shift Law to Solve Differential Equations

Inspired by the method of undetermined coefficients, this paper presents an alternative method to solve linear differential equations with constant coefficients, using the technique of polynomial long division. Expanding this technique with the exponential shift law enables to solve all types of non-homogeneous differential equations, of where the undetermined coefficients can be applied.

The Exact Solution of the Space-Time Fractional Modified Kdv-Zakharov-Kuznetsov Equation

In this paper, we get many new analytical solutions of the space-time nonlinear fractional modified KDV-Zakharov Kuznetsov (mKDV-ZK) equation by means of a new approach namely method of undetermined coefficients based on a fractional complex transform. These solutions have physics meanings in natural sciences. This method can be used to other nonlinear fractional differential equations.

Dispersive optical solitons in DWDM systems

This paper obtains exact bright, dark and singular dispersive optical soliton solutions to DWDM system that is studied with spatio-temporal dispersion in addition to group-velocity dispersion. The governing model is Schrödinger–Hirota equation. The method of undetermined coefficients is employed to secure these soliton solutions that appear with necessary constraints for their existence.

Solving RE models with discontinuous policy rules – an application to minimum wage setting in Germany

ABSTRACTThe legal regulations require the minimum wage in Germany to be adjusted biennially which gives rise to a policy discontinuity. From the perspective of rational expectations models, such policy features render standard local approximation techniques infeasible. The article presents a stylized model in which negotiated wages and corporate profits are the outcome of an optimization problem, while changes to the minimum wage are modelled by a discontinuous policy rule. Using the simple example of minimum wage setting in Germany, the article illustrates how such models can be solved using the method of undetermined coefficients and presents selected simulation results.