We deal with optimal approximation of solutions ODEs under local Lipschitz condition and inexact discrete information about the right-hand side functions. show that randomized two-stage Runge-Kutta scheme is method among all algorithms based on standard noisy information. perform numerical experiments confirm our theoretical findings. Moreover, for algorithm we rigorously investigate properties...

this paper presents approximate analytical solutions for nonlinear oscillators using the multi-step homotopy analysis method (msham). the proposed scheme is only a simple modification of the homotopy analysis method, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. several illustrat...

Recently an implicit method has been presented for solving first order singular initial value problem. The method is extended to solve second or higher order problems having a singular point. The method presents more correct result than those obtained by the implicit Euler and second order implicit Runge-Kutta (RK2) methods. The method is illustrated by suitable examples.

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.

The Multistage Differential Transform Method (MDTM) is employed to solve the model for HIV infection of CD4T cells. Comparing the numerical results to those obtained by the classical fourth order Runge-Kutta method showed the preciseness and efficacy of the multistep differential transform method. The study shows that the method is a powerful and promising tool for solving coupled systems of di...

Radial basis function-Pseudospectral method and Fourier Pseudospectral (FPS) method are extended for stiff nonlinear partial differential equations with a particular emphasis on the comparison of the two methods. Fourth-order Runge-Kutta scheme is applied for temporal discretization. The numerical results indicate that RBF-PS method can be more accurate than standard Fourier pseudospectral meth...