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Operational Jacobi Galerkin method for a class of cordial Volterra integral equations

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Abstract

In this paper, a reliable Jacobi Galerkin method is developed and analyzed to solve a particular class of cordial Volterra integral equations. Existence and uniqueness theorems approve that these kinds of equations possess smooth solutions versus smooth data, so representing their Galerkin solutions based on suitable polynomial basis produces spectrally accurate approximations. Moreover, in order to control condition number growth, we designed a reliable approach that calculates the approximate solutions recursively without solving any high-conditioning systems. Indeed, this approach deals with solving equations in a long integration domain with even high oscillatory solutions. The convergence analysis of the presented approach is established, and the familiar spectral accuracy is justified in \(L_\infty \)-norm. Numerical results are presented to demonstrate the effectiveness of the proposed method. Finally, we provide an application of this method to approximate solution of a two-dimensional case.

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Acknowledgements

The authors would like to thank anonymous referees and editors for their useful comments and suggestions which improved the quality of our paper.

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Author notes

  1. R. Kaafi, P. Mokhtary, and E. Hesameddini contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Shiraz university of Technology, Shiraz, Iran

    R. Kaafi & E. Hesameddini

  2. Department of Mathematics, Faculty of Basic Sciences, Sahand university of Technology, Tabriz, Iran

    P. Mokhtary

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  1. R. Kaafi
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  2. P. Mokhtary
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  3. E. Hesameddini
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Correspondence to P. Mokhtary.

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Kaafi, R., Mokhtary, P. & Hesameddini, E. Operational Jacobi Galerkin method for a class of cordial Volterra integral equations. Numer Algor 96, 827–843 (2024). https://doi.org/10.1007/s11075-023-01667-x

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  • DOI: https://doi.org/10.1007/s11075-023-01667-x

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