scholarly journals A Numerical Scheme For Semilinear Singularly Perturbed Reaction-Diffusion Problems

2020 ◽  
Vol 5 (1) ◽  
pp. 405-412
Author(s):  
Kerem Yamac ◽  
Fevzi Erdogan
Keyword(s):  
Boundary Value Problems ◽  
Numerical Scheme ◽  
Boundary Value ◽  
Reaction Diffusion ◽  
Computational Approach ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Numerical Example ◽  
Uniformly Convergence ◽  
Diffusion Problems

AbstractIn this study we investigated the singularly perturbed boundary value problems for semilinear reaction-difussion equations. We have introduced a basic and computational approach scheme based on Numerov’s type on uniform mesh. We indicated that the method is uniformly convergence, according to the discrete maximum norm, independently of the parameter of ɛ. The proposed method was supported by numerical example.

B-spline Method for Solving General Singularly Perturbed Boundary Value Problems Using Fitted Mesh

2006 ◽  
Vol 2 (4) ◽  
pp. 193-203
Author(s):  
M.K. Kadalbajoo ◽  
Vivek K. Aggarwal
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Point Boundary ◽  
Spline Method ◽  
B Spline ◽  
Linear Problems ◽  
Mesh Technique ◽  
Quasilinearization Technique

In this paper we develop B-spline method for solving a class of Singularly Perturbed two point boundary value problems given as We use the Fitted mesh technique to generate piecewise uniform mesh, and use B-spline method which leads to a tridiagonal linear system. In case of non-linear problems we first linearize the equation using Quasilinearization technique and the resulting problem is solved by B-spline. The convergence analysis is given and the method is shown to have uniform convergence. Numerical illustrations are given in the end to demonstrate the efficiency of our method.

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