full
search.png

Search

close.png

Cancel

arrow
Volume 28, Issue 5
Variable Mesh Finite Difference Method for Self-Adjoint Singularly Perturbed Two-Point Boundary Value Problems

Mohan K. Kadalbajoo & Devendra Kumar

DOI: 10.4208/jcm.1003-m2809

J. Comp. Math., 28 (2010), pp. 711-724.

Published online: 2010-10

Preview Full PDF 1989 22320

Cited by

google scholar semantic scholar
Export citation
  • Abstract

A numerical method based on finite difference method with variable mesh is given for self-adjoint singularly perturbed two-point boundary value problems. To obtain parameter-uniform convergence, a variable mesh is constructed, which is dense in the boundary layer region and coarse in the outer region. The uniform convergence analysis of the method is discussed. The original problem is reduced to its normal form and the reduced problem is solved by finite difference method taking variable mesh. To support the efficiency of the method, several numerical examples have been considered.

  • Keywords

Singularly perturbed boundary value problems, Finite difference method, Boundary layer, Parameter uniform-convergence, Variable mesh.

  • AMS Subject Headings

45Exx, 65L10, 65L12, 65L50, 65L70.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-28-711, author = {}, title = {Variable Mesh Finite Difference Method for Self-Adjoint Singularly Perturbed Two-Point Boundary Value Problems}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {5}, pages = {711--724}, abstract = {

A numerical method based on finite difference method with variable mesh is given for self-adjoint singularly perturbed two-point boundary value problems. To obtain parameter-uniform convergence, a variable mesh is constructed, which is dense in the boundary layer region and coarse in the outer region. The uniform convergence analysis of the method is discussed. The original problem is reduced to its normal form and the reduced problem is solved by finite difference method taking variable mesh. To support the efficiency of the method, several numerical examples have been considered.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1003-m2809}, url = {http://global-sci.org/intro/article_detail/jcm/8545.html} }
TY - JOUR T1 - Variable Mesh Finite Difference Method for Self-Adjoint Singularly Perturbed Two-Point Boundary Value Problems JO - Journal of Computational Mathematics VL - 5 SP - 711 EP - 724 PY - 2010 DA - 2010/10 SN - 28 DO - http://doi.org/10.4208/jcm.1003-m2809 UR - https://global-sci.org/intro/article_detail/jcm/8545.html KW - Singularly perturbed boundary value problems, Finite difference method, Boundary layer, Parameter uniform-convergence, Variable mesh. AB -

A numerical method based on finite difference method with variable mesh is given for self-adjoint singularly perturbed two-point boundary value problems. To obtain parameter-uniform convergence, a variable mesh is constructed, which is dense in the boundary layer region and coarse in the outer region. The uniform convergence analysis of the method is discussed. The original problem is reduced to its normal form and the reduced problem is solved by finite difference method taking variable mesh. To support the efficiency of the method, several numerical examples have been considered.

Mohan K. Kadalbajoo & Devendra Kumar. (1970). Variable Mesh Finite Difference Method for Self-Adjoint Singularly Perturbed Two-Point Boundary Value Problems. Journal of Computational Mathematics. 28 (5). 711-724. doi:10.4208/jcm.1003-m2809
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard