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Alternate Overlapping Schwarz Method for Singularly Perturbed Semilinear Convection-Diffusion Problems

  • S. Chandra Sekhara RaoEmail author
  • Varsha Srivastava
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11189)

Abstract

We propose an alternate overlapping Schwarz method to solve the singularly perturbed semilinear convection-diffusion problems. The method decomposes the original domain into two overlapping subdomains. One, the outside boundary layer subdomain, and the other, inside boundary layer subdomain. On the outside boundary layer subdomain, a combination of the second order compact difference scheme and central difference scheme with uniform mesh is considered; while on the inside boundary layer subdomain a central difference scheme with a special piecewise-uniform mesh is considered. The convergence analysis is given and the method is shown to have almost second order parameter-uniform convergence. Numerical experiments are presented to demonstrate the efficiency of the method.

Keywords

Alternate overlapping Schwarz method Central difference scheme Compact difference scheme Semilinear convection-diffusion problems Singular perturbation problems 

Notes

Acknowledgements

The authors gratefully acknowledge the valuable comments and suggestions from the anonymous referees. The research work of the second author is supported by Council of Scientific and Industrial Research, India.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology DelhiNew DelhiIndia

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