Precise Integration Method for Solving Singular Perturbation Problems

FU Ming-hui; ZHANG Wen-zhi; Sergey V Sheshenin

doi:10.3879/j.issn.1000-0887.2010.11.011

Volume 31 Issue 11

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FU Ming-hui, ZHANG Wen-zhi, Sergey V Sheshenin. Precise Integration Method for Solving Singular Perturbation Problems[J]. Applied Mathematics and Mechanics, 2010, 31(11): 1382-1392. doi: 10.3879/j.issn.1000-0887.2010.11.011

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Precise Integration Method for Solving Singular Perturbation Problems

doi: 10.3879/j.issn.1000-0887.2010.11.011

1.
Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China;

Received Date: 1900-01-01
Rev Recd Date: 2010-09-15
Publish Date: 2010-11-15

Abstract

Abstract

A precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end was presented. Firstly,the interval was divided evenly,then a set of algebraic equations in the form of matrix by the precise integration relationship of each segment was given. Substituting the boundary conditions into the algebraic equations,the coefficient matrix could be transformed to the form of block tridiagonal matrix. Combining the special nature of the problem,an efficient reduction method for singular perturbation problems was given. Since the precise integration relationship gives no discrete error in the discrete process,the present method has very high precision. Numerical examples show the validity of the present method.

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References

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