Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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AN OVERLAPPING SCHWARZ METHOD FOR SINGULARLY PERTURBED THIRD ORDER CONVECTION-DIFFUSION TYPE

  • ROJA, J. CHRISTY (Department of Mathematics, St.Joseph's college) ;
  • TAMILSELVAN, A. (Department of Mathematics, Bharathidasan University)
  • Received : 2017.03.01
  • Accepted : 2018.01.12
  • Published : 2018.01.30
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Abstract

In this paper, an almost second order overlapping Schwarz method for singularly perturbed third order convection-diffusion type problem is constructed. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the combination of classical finite difference scheme and central finite difference scheme on a uniform mesh while on the non-layer region we use the midpoint difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. We proved that, when appropriate subdomains are used, the method produces convergence of second order. Furthermore, it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme are it reduce iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

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References

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