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
Citation: 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

Precise Integration Method for Solving Singular Perturbation Problems

doi: 10.3879/j.issn.1000-0887.2010.11.011
  • Received Date: 1900-01-01
  • Rev Recd Date: 2010-09-15
  • Publish Date: 2010-11-15
  • 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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