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Volume 3, Issue 1
Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid

Jugal Mohapatra & Srinivasan Natesan

DOI: 10.4208/nmtma.2009.m8015

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 1-22.

Published online: 2010-03

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  • Abstract

Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper, we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function. It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter. Numerical experiments illustrate in practice the result of convergence proved theoretically.

  • Keywords

Singular perturbation problems, delay differential equations, boundary layer, upwind scheme, adaptive mesh, uniform convergence.

  • AMS Subject Headings

65L10, 65L12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-3-1, author = {Jugal Mohapatra and Srinivasan Natesan}, title = {Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {1}, pages = {1--22}, abstract = {

Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper, we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function. It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter. Numerical experiments illustrate in practice the result of convergence proved theoretically.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2009.m8015}, url = {http://global-sci.org/intro/article_detail/nmtma/5986.html} }
TY - JOUR T1 - Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid AU - Jugal Mohapatra & Srinivasan Natesan JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 1 EP - 22 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2009.m8015 UR - https://global-sci.org/intro/article_detail/nmtma/5986.html KW - Singular perturbation problems, delay differential equations, boundary layer, upwind scheme, adaptive mesh, uniform convergence. AB -

Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper, we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function. It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter. Numerical experiments illustrate in practice the result of convergence proved theoretically.

Jugal Mohapatra and Srinivasan Natesan. (2010). Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid. Numerical Mathematics: Theory, Methods and Applications. 3 (1). 1-22. doi:10.4208/nmtma.2009.m8015
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