Purely dispersive equations as the Korteweg-de Vries and the nonlinear Schrödinger equation in the limit of small dispersion have solutions to Cauchy problems with smooth initial data which develop a zone of rapid modulated oscillations in the region where the corresponding dispersionless equations have shocks or blowup. Fourth order time-stepping in combination with spectral methods is benefic...

Abstract The main goal of this paper is to developed a high-order and accurate method for the solution one-dimensional generalized Burgers-Fisher with Numman boundary conditions. We combined between fourth-order compact finite difference scheme spatial part diagonal implicit Runge Kutta in temporal part. In addition, we discretized points by using terms fourth order accuracy. This combine leads...

In this paper we consider a new fourth-order method of BDF-type for solving stiff initial-value problems, based on the interval approximation of the true solution by truncated Chebyshev series. It is shown that the method may be formulated in an equivalent way as a Runge–Kutta method having stage order four. Themethod thus obtained have good properties relatives to stability including an unboun...

In this paper we have been discussed the numerical technical solutions for some undamped force vibrations of a spring problem using Runge-Kutta fourth order classical method and Eulers Modified Method. These two methods are very well known in physical mathematical sciences.

A mathematical model is developed and tested with plant data for the ammonia cold shot converter of Razi Petrochemical Complex. The model is based on a material and energy balance in a differential element of beds and is subjected to the assumptions of uniform distribution of temperature and composition through a general cross section and negligible mass and heat transfer in axial direction. Th...

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 ...

In this paper, we present a study of some high-order compact difference schemes for solving the Fitzhugh-Nagumo equations governed by two coupled time-dependent nonlinear reaction diffusion equations in two variables. Solving the Fitzhugh-Nagumo equations is quite challenging, since the equations involve spatial and temporal dynamics in two different scales and the solutions exhibit shock-like ...