Efficient quadrature rules for a class of cordial Volterra integral equations: A comparative study

Document Type : Research Paper

Author

Department of Basic Sciences‎, ‎Iranian Institute for Encyclopedia Research‎, ‎P.O‎. ‎Box 14655-478‎, ‎Tehran‎, ‎Iran.

Abstract

‎A natural algorithm with an optimal order of convergence is proposed for numerical solution of a class of cordial weakly singular Volterra integral equations‎. ‎The equations of this class appear in heat conduction problems with mixed boundary conditions‎. ‎The algorithm is based on a representation of the solution and compound Gaussian quadrature rules with graded meshes‎. ‎A comparative study is carried out‎, ‎which points out that the proposed method is the most efficient one among other existing methods‎. ‎In fact‎, ‎the results of this paper introduce a most-efficient decisive-choice for computing the solution of the heat conduction model‎. 

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References

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Bulletin of the Iranian Mathematical Society
Volume 43, Issue 5
October 2017
Pages 1245-1258

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History

  • Receive Date: 19 December 2015
  • Revise Date: 11 May 2016
  • Accept Date: 20 May 2016

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