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High Accuracy Spline Explicit Group (SEG) Approximation for Two Dimensional Elliptic Boundary Value Problems

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  • Joan Goh
  • Norhashidah Hj. M. Ali

Abstract

Over the last few decades, cubic splines have been widely used to approximate differential equations due to their ability to produce highly accurate solutions. In this paper, the numerical solution of a two-dimensional elliptic partial differential equation is treated by a specific cubic spline approximation in the x-direction and finite difference in the y-direction. A four point explicit group (EG) iterative scheme with an acceleration tool is then applied to the obtained system. The formulation and implementation of the method for solving physical problems are presented in detail. The complexity of computational is also discussed and the comparative results are tabulated to illustrate the efficiency of the proposed method.

Suggested Citation

  • Joan Goh & Norhashidah Hj. M. Ali, 2015. "High Accuracy Spline Explicit Group (SEG) Approximation for Two Dimensional Elliptic Boundary Value Problems," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-13, July.
    • Handle: RePEc:plo:pone00:0132782
    DOI: 10.1371/journal.pone.0132782
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