Mathematics of Computation
Solving singularly perturbed boundary-value problems by spline in tension
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Singular perturbation methods for ordinary differential equations
Singular perturbation methods for ordinary differential equations
A computational method for solving singular perturbation problems
Applied Mathematics and Computation
A computational method for solving quasilinear singular perturbation problems
Applied Mathematics and Computation
Applied Mathematics and Computation
A computational method for self-adjoint singular perturbation problems using quintic spline
Computers & Mathematics with Applications
Solving singular perturbation problems by b-spline and artificial viscosity method
ICICA'11 Proceedings of the Second international conference on Information Computing and Applications
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A class of singularly perturbed two point boundary value problems (BVPs) for second order ordinary differential equations in self-adjoint form arising in the study of chemical catalysis and Michaelis-Menten process in biology is considered. In order to solve them, a numerical method as in [Appl. Math. Comput. 55 (1993) 31] is proposed. The essential idea in this method is to divide the domain of the differential equation into three non-overlapping subdomains and solve the given equations over these regions separately as three two-point BVPs numerically. The inner region problems are solved using a fitted operator method [Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole press, Dublin, 1980], whereas the outer region problem is solved using a classical central difference method. The boundary conditions at the transition points are obtained using the zero order asymptotic expansion approximation to the solution of the problem. This method is well suited for parallel computing and an algorithm for the same is given. Error estimates are derived for the numerical solution. Some schemes for self-adjoint equations in conservation form are given. Using Newton's method of quasilinearization, a class of semilinear problems are also solved. Numerical experiments are conducted. It is found that the present method performs better than the fitted mesh method [Fitted Numerical Methods for Singular Perturbation Problems, World Scientific, Singapore, 1996] and higher order method [Numeriche Mathematik 56 (1990) 675].