Linear Test Equation Research Articles

Pengaruh Loan To Deposit Ratio (LDR) Dan Non Perfoming Loan (NPL) Terhadap Harga Saham Pada PT Bank Negara Indonesia (Persero) Tbk Periode 2013-2022

This research aims to determine the effect of Loan to Deposit Ratio (LDR) and Non-Performing Loans (NPL) on stock at PT Bank Negara Indonesia (BNI) Tbk for 2013-2022. This research uses 2 (two) independent variables That is Loan to Deposit Ratio (LDR) and Non Performing Loan (NPL) and 1 (one) dependent variable stock's price. This research is using quantitative methods, data analysis uses descriptive statistical techniques, classical assumption tests, multiple linear regression, hypothesis testing and coefficient of determination. Data processing uses SPPS 26 software. Based on test results on variables with 10 years of data. The Multiple Linear Regression Test Equation is Y = 19,248.185 – 106.314X1 – 1,563.302X2. In the coefficient of determination test, it was found that the influence of LDR and NPL on share prices was 10%, while the remaining 90% was influenced by other factors. Based on the results of the t test, tcount for LDR was 0.612 < ttable 2.365 and the value of Sig. 0.560 > 0.05 means that there is no partial significant influence between LDR on share prices. and NPL tcount of 0.872 < ttable 2.365 and Sig value. 0.412 > 0.05, which means that there is no partial significant influence between NPL on share prices. In the simultaneous test the LDR and NPL variables do not have a significant effect on share prices with Fcount being smaller than Ftable (0.693 < 4.74).

ANALISIS PENGARUH STORE ATMOSPHERE TERHADAP KEPUTUSAN PEMBELIAN DI KOPI JAGA CIREBON

In 2019 Kopi Jaga Cirebon joined the cafe industry in Indonesia and succeeded in surviving until now for a period of 4 years. Kopi Jaga Cirebon always maintains its existence in the sector of coffee drinks and non-coffee. In preserving its existence, Kopi Jaga Cirebon also creates a comfortable cafe atmosphere equipped with public facilities so that Kopi Jaga Cirebon customers can enjoy drinks while relaxing at Kopi Jaga Cirebon. This research was conducted to find out how influential the store atmosphere towards the customers' purchasing decisions at Kopi Jaga Cirebon. To find out this, the researcher conducted the study using a quantitative method using multiple linear regression analysis along with the result of the Hypothesis Test. The researcher used ways by spreading questionnaires and observation for collecting data. The result of the T-test is T count > T table. Then, the significance value is 0.00 < 0.05. Therefore, the store atmosphere gives some positive effects on the purchasing decisions at Kopi Jaga Cirebon. The formulation of the multiple linear regression test equation is Y = 11.401+0.240X1+0.167X2+0.640X3+0.145X4 wherein every time there is a store atmosphere there will be an increase of 34.6% to the purchasing decision obtained from the test results of the coefficient of determination. The conclusion is that store atmosphere influences purchasing decisions at Kopi Jaga Cirebon so that managers can maintain and improve each indicator of the store atmosphere (X) to improve each indicator on purchasing decisions (Y).

Simulating systems of Itô SDEs with split-step $ (\alpha, \beta) $-Milstein scheme

<abstract><p>In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step $ (\alpha, \beta) $-Milstein scheme strongly convergence to the exact solution with order $ 1.0 $ in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters $ \alpha, \beta $. Finally, numerical examples illustrate the effectiveness of the theoretical results.</p></abstract>

Milstein method for solving fuzzy differential equation

To solve fuzzy differential equations driven by Liu process, three Milstein schemes are proposed in this work, which are explicit Milstein scheme, semi-implicit Milstein scheme and improved Milstein scheme. Improved Milstein scheme is constructed by correcting the error with semi-implicit method, the error is the difference between the exact solution of fuzzy differential equations and the solution derived from Milstein scheme. These numerical methods are proved to have strong convergence with order two. Accompanying the results above, the concept of mean-stability of numerical schemes for fuzzy differential equations is put forward and analyzed. For a linear test equation, it is showed the mean-stability region of improved Milstein scheme is bigger than explicit Milstein scheme. Finally, the accuracy and effectiveness of these schemes are confirmed through numerical examples.

(2002-5686) Milstein method for solving fuzzy differential equation

To solve fuzzy differential equations driven by Liu process, three Milstein schemes are proposed in this work, which are explicit Milstein scheme, semi-implicit Milstein scheme and improved Milstein scheme. Improved Milstein scheme is constructed by correcting the error with semi-implicit method, the error is the difference between the exact solution of fuzzy differential equations and the solution derived from Milstein scheme. These numerical methods are proved to have strong convergence with order two. Accompanying the results above, the concept of mean-stability of numerical schemes for fuzzy differential equations is put forward and analysed. For a linear test equation, it is showed the mean-stability region of improved Milstein scheme is bigger than explicit Milstein scheme. Finally, the accuracy and effectiveness of these schemes are confirmed through numerical examples.

Second-order balanced stochastic Runge–Kutta methods with multi-dimensional studies

In this paper, we have considered two classes of second-order balanced stochastic Runge–Kutta methods to multidimensional Itô stochastic differential equations. The control functions in the proposed methods are used to improve and enhance the convergence and stability properties of the method. The strong convergence of the second-order balanced stochastic Runge–Kutta methods is analyzed. The preservation of sign of initial value to the second order balanced stochastic Runge–Kutta methods for a linear scalar test equations is discussed under suitable conditions. Moreover, the mean-square stability of the proposed methods is investigated using the properties of Kronecker product. Subsequently the stability region of the balanced stochastic Runge–Kutta methods for s=4 stages is compared with the other existing stochastic Runge–Kutta methods. From this comparison, we understood the balanced stochastic Runge–Kutta methods are more stable than the stochastic Runge–Kutta methods. Finally, the mean square stability for different step sizes h is illustrated as well convergence results compared with other current methods are tabulated.

Study of micro–macro acceleration schemes for linear slow-fast stochastic differential equations with additive noise

Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims at resolving the statistics of the slowest dynamics. This paper looks at the efficiency of a micro-macro acceleration method that couples short bursts of stochastic path simulation with extrapolation of spatial averages forward in time. To have explicit derivations, we elicit an amenable linear test equation containing multiple time scales. We make derivations and perform numerical experiments in the Gaussian setting, where only the evolution of mean and variance matters. The analysis shows that, for this test model, the stability threshold on the extrapolation step is largely independent of the time-scale separation. In consequence, the micro-macro acceleration method increases the admissible time steps far beyond those for which a direct time discretization becomes unstable.

Compensated θ-Milstein methods for stochastic differential equations with Poisson jumps

In this paper, we are concerned with numerical methods for solving stochastic differential equations with Poisson-driven jumps. We construct a class of compensated θ-Milstein methods and study their mean-square convergence and asymptotic mean-square stability. Sufficient and necessary conditions for the asymptotic mean-square stability of the compensated θ-Milstein methods when applied to a scalar linear test equation are derived. We compare the asymptotic mean-square stability region of the linear test equation with that of the compensated θ-Milstein methods with different θ values. Numerical results are given to verify our theoretical results.

Stability analysis of high order Runge–Kutta methods for index 1 stochastic differential-algebraic equations with scalar noise

In this paper, a new class of implicit stochastic Runge-Kutta (SRK) methods is constructed for numerically solving systems of index 1 stochastic differential-algebraic equations (SDAEs) with scalar multiplicative noise. By applying rooted tree theory analysis, the family of coefficients of the proposed methods of order 1.5 are calculated in the mean-square sense. In particular, we derive some four-stage stiffly accurate semi-implicit SRK methods for approximating index 1 SDAEs with scalar noise. For these methods, first, MS-stability functions, applied to a scalar linear test equation with multiplicative noise, are calculated. Then, their regions of MS-stability are compared with the corresponding MS-stability region of the original SDE. Accordingly, we illustrate that the proposed schemes seems to have good stability properties. Numerical results will be presented to check the convergence order and computational efficiency of the new methods.

Slow-scale split-step tau-leap method for stiff stochastic chemical systems

Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. Motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and systems biology. It is known that the dynamical behavior of biochemical systems is often intrinsically stiff representing a serious challenge for their numerical approximation. The naive extension of stiff deterministic solvers to stochastic integration often yields numerical solutions with either impractically large relaxation times or incorrectly resolved covariance. In this paper, we propose a splitting heuristic which helps to resolve some of these issues. The proposed integrator contains a number of unknown parameters which are estimated for each particular problem from the moment equations of the corresponding linearized system. We show that this method is able to reproduce the exact mean and variance of the linear scalar test equation and demonstrates a good accuracy for the arbitrarily stiff systems at least in the linear case. The numerical examples for both linear and nonlinear systems are also provided and the obtained results confirm the efficiency of the considered splitting approach.

Convergence and Stability of Split-Step-Theta Methods for Stochastic Differential Equations With Jumps Under Non-Global Lipschitz Coefficients

In this paper, we investigate the convergence and stability of the split step theta method (SSTM) and its compensated form for stochastic differential equations with jumps (SDEwJs) under non-global Lipschitz condition of the drift term. The methods converge strongly to the exact solution in the root mean square with order 1/2. Stability analysis reveals that the compensated split-step-theta method (CSSTM) holds the A-stability property for θ ∈ [1/2, 1] for both linear and nonlinear cases. For a linear test equation with a negative drift and positive jump coefficients, there exists θ ≤ 1/2 for which the SSTM is A-stable. This overcome the barrier of θ by D. J. Higham & P. E. Kloeden (2006) and X. Wang & S. Gan (2010). In the nonlinear case the SSTM holds the B-stability property. We give some numerical experiments to illustrate our theoretical results.

Stability of Numerical Solutions for Abel–Volterra Integral Equations of the Second Kind

We analyze the stability of convolution quadrature methods for weakly singular Volterra integral equations with respect to a linear test equation. We prove that the asymptotic behavior of the numerical solution replicates the one of the continuous problem under some restriction on the stepsize. Numerical examples illustrate the theoretical results.

A Lyapunov and Sacker–Sell spectral stability theory for one-step methods

Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly, exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.

Asymptotic mean-square stability of weak second-order balanced stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential systems

In this paper, the linear asymptotic mean-square stability of the weak second-order stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential equations due to Rößler (2009) and Tang and Xiao (2017) are obtained. Further, we have developed the stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential equations to the balanced stochastic Runge–Kutta methods by using the control functions. We carry out a linear stability analysis of the class of stochastic Runge–Kutta methods for the linear test equations with multiplicative noise thereby providing an explicit structure of stability matrices. Some comparisons and illustrations shows that there is an improvement in the stability and error analysis of these new balanced stochastic Runge–Kutta methods comparatively to stochastic Runge–Kutta methods and thus conforming the obtained theoretical results.

A new spline in compression method of order four in space and two in time based on half-step grid points for the solution of the system of 1D quasi-linear hyperbolic partial differential equations

In this paper, we propose a new three-level implicit method based on a half-step spline in compression method of order two in time and order four in space for the solution of one-space dimensional quasi-linear hyperbolic partial differential equation of the form u_{tt} =A(x,t,u)u_{xx} +f(x,t,u,u_{x},u_{t}). We describe spline in compression approximations and their properties using two half-step grid points. The new method for one-dimensional quasi-linear hyperbolic equation is obtained directly from the consistency condition. In this method we use three grid points for the unknown function u(x,t) and two half-step points for the known variable ‘x’ in x-direction. The proposed method, when applied to a linear test equation, is shown to be unconditionally stable. We have also established the stability condition to solve a linear fourth-order hyperbolic partial differential equation. Our method is directly applicable to solve hyperbolic equations irrespective of the coordinate system, which is the main advantage of our work. The proposed method for a scalar equation is extended to solve the system of quasi-linear hyperbolic equations. To assess the validity and accuracy, the proposed method is applied to solve several benchmark problems, and numerical results are provided to demonstrate the usefulness of the proposed method.

Weak Second Order Explicit Exponential Runge--Kutta Methods for Stochastic Differential Equations

We propose new explicit exponential Runge--Kutta methods for the weak approximation of solutions of stiff Ito stochastic differential equations (SDEs). We also consider the use of exponential Runge--Kutta methods in combination with splitting methods. These methods have weak order 2 for multidimensional, noncommutative SDEs with a semilinear drift term, whereas they are of order 2 or 3 for semilinear ordinary differential equations. These methods are A-stable in the mean square sense for a scalar linear test equation whose drift and diffusion terms have complex coefficients. We carry out numerical experiments to compare the performance of these methods with an existing explicit stabilized method of weak order 2.

Exponential mean-square stability of the improved split-step theta methods for non-autonomous stochastic differential equations

We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with real parameters. When θ ≥ 3/2, the improved split-step theta methods can reproduce the mean-square stability of the linear test equations for any step sizes h > 0. Then, under a coupled condition on the drift and diffusion coefficients, we consider exponential mean-square stability of the method for nonlinear non-autonomous stochastic differential equations. Finally, the obtained results are supported by numerical experiments.

Stability analysis of explicit exponential integrators for delay differential equations

The aim of this paper is to analyze stability properties of explicit exponential integrators for three kinds of delay differential equations. First, linear autonomous delay differential equations are studied, and sufficient conditions for P- and GP-contractivity of explicit exponential Runge–Kutta methods are given. Second, for linear nonautonomous test equations, PN- and GPN-stability of a particular Magnus integrator is investigated. It is shown that the Magnus integrator is GPN-stable and convergent of order two. Finally, for semilinear delay differential equations, RN- and GRN-stability of explicit exponential Runge–Kutta methods is studied and sufficient conditions for GRN-stability are derived. Some examples of P-, GP-, RN- and GRN-stable exponential integrators are given, and numerical experiments that illustrate the theoretical results are included.

An improved Milstein method for stiff stochastic differential equations

To solve the stiff stochastic differential equations, we propose an improved Milstein method, which is constructed by adding an error correction term to the Milstein scheme. The correction term is derived from an approximation of the difference between the exact solution of stochastic differential equations and the Milstein continuous-time extension. The scheme is proved to be strongly convergent with order one and is as easy to implement as standard explicit schemes but much more efficient for solving stiff stochastic problems. The efficiency and the advantage of the method lie in its very large stability region. For a linear scalar test equation, it is shown that the mean-square stability domain of the method is much bigger than that of the Milstein method. Finally, numerical examples are reported to highlight the accuracy and effectiveness of the method.

Almost sure exponential stability of an explicit stochastic orthogonal Runge-Kutta-Chebyshev method for stochastic delay differential equations

Compared with Euler-Maruyama type schemes, there is a lack of studies on the stability of Runge-Kutta type methods applied to stochastic delay differential equations (SDDEs). This paper is concerned with filling this imbalance. The focus is on the almost sure exponential stability of an explicit stochastic Runge-Kutta-Chebyshev (S-ROCK) method for an Ito-type linear test equation, which is analyzed by applying the techniques based on a discrete semimartingale convergence theorem.