A high-order accurate, finite-difference method for the numerical solution of the incompressible Navier–Stokes equations is presented. Fourth-order accurate discretizations of the convective and viscous fluxes are obtained on staggered meshes using explicit or compact finite-difference formulas. High-order accuracy in time is obtained by marching the solution with Runge–Kutta methods. The incom...

In this paper, two different numerical schemes, namely the Runge-Kutta fourth order method and the implicit Euler method with perturbation method of the second degree, are applied to solve the nonlinear thermal wave in one and two dimensions using the differential quadrature method. The aim of this paper is to make comparison between previous numerical schemes and detect which is more efficient...

A new explicit fourth-order six-stage Runge-Kutta scheme with low dispersion and low dissipation properties is developed. This new Runge-Kutta scheme is shown to be more efficient in terms of dispersion and dissipation properties than existing algorithms such as Runge-Kutta temporal schemes developed by Hu et al. (1996), Mead and Renaut (1999), Tselios and Simos (2005). We perform a spectral an...

In this work, Differential Transform Method (DTM) was employed to obtain the series solution of SIRV COVID-19 model in Nigeria. The validity DTM solving validated by Maple 21’s Classical fourth-order Runge-Kutta method. comparison between and Runge- Kutta (RK4) solutions performed there a good correlation results obtained two methods. result validates accuracy efficiency solve

A fourth-order, implicit, low-dispersion, and low-dissipation Runge-Kutta scheme is introduced. The scheme is optimized for minimal dissipation and dispersion errors. High order accuracy is achieved with fewer stages than standard explicit Runge-Kutta schemes. The scheme is designed to be As table for highly stiff problems. Possible applications include wall-bounded flows with solid boundaries ...

A modified Boris-like integration, in which the spatial coordinate is the independent variable, is derived. This spatial-Boris integration method is useful for beam simulations, in which the independent variable is often the distance along the beam. The new integration method is second order accurate, requires only one force calculation per particle per step, and preserves conserved quantities ...

A method is presented to easily derive von Neumann stability conditions for a wide variety of time discretization schemes for the convection-di usion equation. Spatial discretization is by the -scheme or the fourth order central scheme. The use of the method is illustrated by application to multistep, Runge-Kutta and implicit-explicit methods, such as are in current use for ow computations, and...

In this article, a multistage homotopy perturbation method is employed to solve a system of nonlinear differential equations, namely Coullet system. Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. It is shown that the proposed method is robust, accurate and easy to apply.