A Parameter-Uniform B-Spline Collocation Method for Singularly Perturbed Semilinear Reaction-Diffusion Problems

2010 ◽  
Vol 146 (3) ◽  
pp. 795-809 ◽  
Author(s):  
S. C. S. Rao ◽  
S. Kumar ◽  
M. Kumar
Keyword(s):  
Collocation Method ◽  
Reaction Diffusion ◽  
Singularly Perturbed ◽  
Spline Collocation ◽  
B Spline ◽  
Spline Collocation Method ◽  
Diffusion Problems

B-SPLINE COLLOCATION METHOD FOR A SINGULARLY PERTURBED REACTION–DIFFUSION PROBLEM USING ARTIFICIAL VISCOSITY

2009 ◽  
Vol 06 (01) ◽  
pp. 23-41 ◽  
Author(s):  
MOHAN K. KADALBAJOO ◽  
PUNEET ARORA
Keyword(s):  
Exact Solution ◽  
Collocation Method ◽  
Reaction Diffusion ◽  
Artificial Viscosity ◽  
Reaction Diffusion Equations ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Spline Collocation ◽  
B Spline ◽  
Spline Collocation Method

In this paper, we develop a B-spline collocation method using artificial viscosity for solving a class of singularly perturbed reaction–diffusion equations. We use the artificial viscosity to capture the exponential features of the exact solution on a uniform mesh, and use the B-spline collocation method, which leads to a tridiagonal linear system. The convergence analysis is given and the method is shown to have uniform convergence of second order. The design of an artificial viscosity parameter is confirmed to be a crucial ingredient for simulating the solution of the problem. Known test problems have been studied to demonstrate the accuracy of the method. Numerical results show the behavior of the method, with emphasis on treatment of boundary conditions. Results shown by the method are found to be in good agreement with the exact solution.

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