Variable mesh non polynomial spline method for singular perturbation problems exhibiting twin layers

Abstract

In this paper, we descend a variable mesh finite difference scheme based on non polynomial spline approximation for the solution of singular perturbation problems with twin boundary layers. We develop the discretization equation for the problem using the condition of continuity for the first order derivatives of the variable mesh non polynomial spline at the interior nodes. The discrete invariant imbedding algorithm is utilized to solve the tridiagonal system obtained by the method. Endeavor examples are illustrated and maximum absolute errors in comparison to the other methods in the literature are shown to vindicate the method.

Swarming procedures to solve the novel perturbed delay third order singular model

“…As a result, some reliable numerical techniques should be developed to deal such kinds of mathematical problems [1][2][3][4][5][6]. An exponential fitting and finite differences computing techniques have been presented to solve the singular perturbed type of model [7][8][9]. Some investigations that have been presented to solve the 2 nd order perturbed diffusion/convection system through the mesh approach along with the semi-linear diffusion/ reaction [8,[10][11][12].…”

A Numerical Scheme For Semilinear Singularly Perturbed Reaction-Diffusion Problems

“…It can be found in the literature that there are many numerical finite difference schemes that are stable for all values parameter of perturbation [2][3][4][5][6][7][8][9]. One of the most important ways to easily find the methods that give such results is use of finite difference schemes with exponentially fitted [11][12][13].…”

“…The Numerov method is undoubtedly one of the most well known methods for reaction-diffusion type equations since it has fourth-order approach and it has been widely used in practical computational methods. Recently much fitted dinite difference scheme has been studied based on Numerov's method in [11][12][13][14][15][16][17][18]. In [11], Phaneendra et al gave a finite difference Numerov scheme with a fitted multiplier three bands for solving singularly perturbed boundary value problem.…”

“…Recently much fitted dinite difference scheme has been studied based on Numerov's method in [11][12][13][14][15][16][17][18]. In [11], Phaneendra et al gave a finite difference Numerov scheme with a fitted multiplier three bands for solving singularly perturbed boundary value problem. Based on Numerov method, singularly perturbed nonlinear reaction-diffusion problem were investigated in [16][17][18][19].…”

A neuro swarm procedure to solve the novel second order perturbed delay Lane-Emden model arising in astrophysics

“…Consequently, it is the need of the time to design some reliable numerical schemes for such models [1][2][3][4][5][6][7] . A computing scheme using the finite difference and the exponential fitting is explored to achieve the performances of the singular perturbed form of the models [8][9][10] . Some other schemes presented to solve the convection-diffusion second order perturbed singular delay differential model (SO-PSDDM) 11 .…”