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High order fitted operator numerical method for self-adjoint singular perturbation problems
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DOI：10.1016/j.amc.2005.01.069.png)
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摘要
En 中文
We consider self-adjoint singularly perturbed two-point boundary value problems in conservation form. Highest possible order of uniform convergence for such problems achieved hitherto, via fitted operator methods, was one (see, e.g., [Doolan et al. Uniform numerical methods for problems with initial and boundary layers, Boole Press, Dublin, 1980], p. 121]). Reducing the original problem into the normal form and then using the theory of inverse monotone matrices, a fitted operator finite difference method is derived via the standard Numerov's method. The scheme thus derived is fourth order accurate for moderate values of the perturbation parameter E whereas for very small values of this parameter the method is epsilon-uniformly convergent with order two. Numerical examples are given in support of the theory. (c) 2005 Elsevier Inc. All rights reserved.
Keyword:
singular perturbation problems
ordinary differential equations
boundary value problems
finite difference methods
fitted operator methods
Numerov's method
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期刊
IF:
3.4
论文数:
2.3W
被引数:
3.3W
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A survey of numerical techniques for solving singularly perturbed ordinary differential equations
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