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...

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, we use the spectral collocation method based on Chebyshev polynomials for spatial derivatives and fourth order Runge-Kutta (RK) method for time integration to solve the generalized Zakharov equation (GZE). Firstly, theory of application of Chebyshev spectral collocation method on the GZE is presented. This method yields a system of ordinary differential equations (ODEs). Secondly...

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...

An optimized explicit low-storage fourth-order Runge–Kutta algorithm is proposed in the present work for time integration. Dispersion and dissipation of the scheme are minimized in the Fourier space over a large range of frequencies for linear operators while enforcing a wide stability range. The scheme remains of order four with nonlinear operators thanks to the low-storage algorithm. Linear a...

Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi‐ step integration methods. The coefficients are reverse engineered based on samples from a target function and its derivative used for training. The Runge‐Kutta schemes are tra...

Strong stability-preserving (SSP) Runge–Kutta methods were developed for time integration of semidiscretizations of partial differential equations. SSP methods preserve stability properties satisfied by forward Euler time integration, under a modified time-step restriction. We consider the problem of finding explicit Runge–Kutta methods with optimal SSP time-step restrictions, first for the cas...

The aim of this article is to model and analyze an unsteady axisymmetric flow of non-conducting, Newtonian fluid squeezed between two circular plates passing through porous medium channel with slip boundary condition. A single fourth order nonlinear ordinary differential equation is obtained using similarity transformation. The resulting boundary value problem is solved using Homotopy Perturbat...

An embedded diagonally implicit Range-Kutta Nystrom (RKN) method is constructed for the integration of initial value problems for second order ordinary differential equations possessing oscillatory solutions. This embedded method is derived using a three stage diagonally implicit Runge-Kutta Nystrom method of order four within which a third order three stage diagonally implicit Runge-Kutta Nyst...

This paper presents a family of Runge{Kutta type integration schemes of arbitrarily high order for di erential equations evolving on manifolds. We prove that any classical Runge{Kutta method can be turned into an invariant method of the same order on a general homogeneous manifold, and present a family of algorithms that are relatively simple to implement.