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Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary Conditions

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  • Mohamed E. A. Alnair
  • Ahmed A. Khidir
  • Yufeng Xu

Abstract

This paper presents a new technique for solving linear Volterra integro-differential equations with boundary conditions. The method is based on the blending of the Chebyshev spectral methods. The application of the proposed method leads the Volterra integro-differential equation to a system of algebraic equations that are easy to solve. Some examples are introduced and the obtained results are compared with exact solution as well as the methods that reported in the literature to illustrate the effectiveness and accuracy of the method. The results demonstrate that there is congruence between the numerical and the exact results to a high order of accuracy. Tables were generated to verify the accuracy convergence of the method and error. Figures are presented to show the excellent agreement between the results of this study and the results from literature.

Suggested Citation

  • Mohamed E. A. Alnair & Ahmed A. Khidir & Yufeng Xu, 2022. "Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary Conditions," Abstract and Applied Analysis, Hindawi, vol. 2022, pages 1-14, April.
    • Handle: RePEc:hin:jnlaaa:2217882
    DOI: 10.1155/2022/2217882
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