In current study, the modified variational iteration algorithm-I is investigated in the form of the
analytical and numerical treatment of different types of nonlinear partial differential …

In this paper a numerical method is proposed to approximate the solution of the nonlinear
Burgers' equation. The method is based on collocation of modified cubic B-splines over finite …

In this paper, a class of high-order compact difference method is introduced for solving the
Burgers' equations. Firstly, a linear high-order compact difference scheme is proposed to …

In this paper, we have applied modified cubic B-spline based differential quadrature method
to get numerical solutions of one dimensional reaction-diffusion systems such as linear …

The aim of this paper is to obtain numerical solutions of the one-dimensional, two-
dimensional and coupled Burgers' equations through the generalized differential quadrature …

In the present paper, we derive the solution of the nonlinear fractional partial differential
equations using an efficient approach based on the q-homotopy analysis transform method …

In this paper, a numerical method is proposed to approximate the solution of the nonlinear
parabolic partial differential equation with Neumann's boundary conditions. The method is …

This study presents a comprehensive analytical approach to address the complexities of
flow and heat transfer in planar Taylor–Couette systems. Utilizing innovative simplifying …

In this work, accurate solutions to linear and nonlinear diffusion equations were introduced.
A combination of a sixth-order compact finite difference scheme in space and a low-storage …

This article proposes a family of non-standard methods coupled with compact finite
differences to numerically integrate the non-linear Burgers' equation. Firstly, a family of non …