ISSN 2234-8417 (Online) ISSN 1598-5857 (Print)

Table of Contents
2018's   36, 1-2(Jan)
  An overlapping Schwarz method for singularly perturbed third
    By J. Christy Roja ..........1774
Generic Number - 1774
References - 19
Written Date - January 30th, 18
Modified Date - January 30th, 18
Downloaded Counts - 113
Visited Counts - 639
Original File
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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