Integrating various suppliers to satisfy market demand is of great importance for e ective supply chain management. In this paper, we consider the ODE-PDE model of supply chain and apply a classical explicit fourth-order Runge-Kutta scheme for the related ODE model of suppliers. Also, the convergence of the proposed method is proved. Finally a numerical example is studied to demonstrate the acc...

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the...

We present benchmark simulations for the 8:1 di erentially heated cavity problem, the focus of a special session at the rst MIT conference on Computational Fluid and Solid Mechanics in June 2001. The numerical scheme is a fourth-order nite di erence method based on the vorticity-stream function formulation of the Boussinesq equations. The momentum equation is discretized by a compact scheme wit...

To analyze a harmonically Van der Pol oscillator, this work used combination of graphs, time steps distribution, adaptive Runge-Kutta, and fourth order algorithms. The goal is to examine the performance third Runge-Kutta algorithms in finding chaotic solutions for excited oscillator. Fourth-order favor larger are thus faster execute than third-order all circumstances studied. accuracy data acqu...

Efficient solution techniques for high-order accurate time-dependent problems are investigated for solving the two-dimensional non-linear Euler equations in this work. The spatial discretization consists of a high-order accurate Discontinuous Galerkin (DG) approach. Implicit time-integration techniques are considered exclusively in order to avoid the stability restrictions of explicit methods. ...

In this paper, numerical simulations of nonlinear Fisher’s equation in oneand twodimensions have been considered. The derivatives and integrals are replaced by the necessary matrices, and the resulting algebraic system of equations was advanced by the popular fourth-order exponential time differencing Runge-Kutta (ETDRK4) schemes proposed by Cox and Matthew [Exponential time differencing for st...

in this paper, homotopy perturbation method (hpm) has been applied to investigate the effect of magnetic field on cu-water nanofluid flow in non-parallel walls. the validity of hpm solutions were verified by comparing with numerical results obtained using a fourth order runge–kutta method. effects of active parameters on flow have been presented graphically. the results show that velocity in bo...

This article extends the theory of classical finite-difference summation-by-parts (FD-SBP) timemarching methods to the generalized summation-by-parts (GSBP) framework. Dual-consistent GSBP time-marching methods are shown to retain: A and L-stability, as well as superconvergence of integral functionals when integrated with the quadrature associated with the discretization. This also implies that...

A family of predictor-corrector exponential Numerov-type methods is developed for the numerical integration of the one-dimensional Schrr odinger equation. The formula considered contains certain free parameters which allow it to be tted automatically to exponential functions. The new methods are very simple and integrate more exponential functions than both the well known fourth order Numerov t...