Year: 2010
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 3 : pp. 535–548
Abstract
A system of singularly perturbed ordinary differential equations of first order with given initial conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These parameters are assumed to be distinct and they determine the different scales in the solution to this problem. A Shishkin piecewise-uniform mesh is constructed, which is used, in conjunction with a classical finite difference discretization, to form a new numerical method for solving this problem. It is proved that the numerical approximations obtained from this method are essentially first order convergent uniformly in all of the parameters. Numerical results are presented in support of the theory.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-IJNAM-736
International Journal of Numerical Analysis and Modeling, Vol. 7 (2010), Iss. 3 : pp. 535–548
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Linear dynamical system multiscale initial value problem singularly perturbed finite difference method parameter-uniform convergence.