Solution of second order nonlinear singular perturbation ordinary differential equation based on the Samarskii scheme
A.I. Zadorin, S.V. Tikhovskaya
Keywords: second order nonlinear ordinary differential equation, singular perturbation, Newton method, Picard method, Samarskii scheme, Shishkin mesh, uniform convergence, two-grid algorithm
Abstract
A boundary value problem for a second order nonlinear singular perturbation ordinary differential equation is considered. We propose the method based on the Newton and the Picard linearizations using known modified Samarskii scheme on the Shishkin mesh in the case of a linear problem. It is proved that the constructed difference schemes are of second order and uniformly convergent. To decrease the number of the arithmetical operations, we propose a two-grid method. The results of some numerical experiments are discussed.
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