Computational study for a class of time-dependent singularly perturbed parabolic partial differential equation through tension spline

Abstract

This article contributes a numerical technique for a class of singularly perturbed time delayed parabolic partial differential equation. A priori results of maximum principle, stability and bounds are discussed. The continuous problem is semi-discretized by the Crank-Nicolson based scheme in the temporal direction and then discretized by the tension spline scheme on non-uniform Shishkin mesh. Error estimation for the discretized problem is derived. To validate the theoretical findings, the numerical outcomes for linear and nonlinear problems are tested.

The Solution of Fractional Diffusion-reaction Equation Via the Regular Perturbation Method (RPM)

“…Thus, this solution is the same as that obtain by Y. Minougou in his thesis [1], [2], [3], [4], [5] where he used the Adomian method with α = 1.…”

“…Secondly, we will compare the solutions obtained with the solutions resulting from another resolution method in a previous search for a given value of α. α is defined in the problem below. Searchers such as Y. MINOUGOU have already solved the case where α = 1 with several methods [1,2,3,4,5].…”

A uniformly convergent numerical scheme for solving singularly perturbed differential equations with large spatial delay

“…Cimen [13] treated singularly perturbed differential equation with delay and advance by constructing a scheme by the method of integral identities with the use of interpolating quadrature rules. Kumar and Kanth [14] solved time dependent singularly perturbed differential equation using tension spline on a non-uniform Shishkin mesh. Adilaxmi and Reddy [15] solved singularly perturbed differential-difference equations applying an initial value technique via fitted nonstandard finite difference method.…”