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Existence and computational results to Volterra–Fredholm integro-differential equations involving delay term

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Abstract

The present article is concerned with deriving necessary conditions for the existence theory of solution to a class of delay Fredholm–Volterra integro-differential equations using fixed point approach. Also via the use of the Haar collocation method, a numerical scheme is established. With the help of the mentioned method the considered problem is transformed into a system of algebraic equations which is then solved for the required results by using Gauss elimination algorithm. Further the necessary conditions required for a numerical technique to be held like maximum absolute errors, efficacy and comparison with exact solution as well as with the results of other numerical schemes are performed by taking various numbers of collocation points. The obtained results are compared with the results of the Spline functions algorithm for the concerned problems. Various pertinent test problems are given to testify the results.

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Acknowledgements

We all authors are very thankful to the reviewers for their useful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of Peshawar, Peshawar, 25120, Khyber Pakhtunkhwa, Pakistan

    Rohul Amin

  2. Institute of IR 4.0 The National University of Malaysia, Selangor, Malaysia

    Ali Ahmadian

  3. Department of Mathematics, Near East University Nicosia, TRNC, Mersin 10, Turkey

    Ali Ahmadian

  4. Department of Mathematics, Northern Borders University, Turaif, Saudi Arabia

    Nasser Aedh Alreshidi

  5. Department of Computational Mathematics, School of Sciences China University of Petroleum, Qingdoo, 266555, China

    Liping Gao

  6. Department of Mathematics and Statistics, St. Francis Xavier University, Antigonish, NS, Canada

    Mehdi Salimi

  7. Center for Dynamics, Faculty of Mathematics, Technische Universität Dresden, Dresden, Germany

    Mehdi Salimi

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  1. Rohul Amin
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All authors equally contributed this manuscript and approved the final version.

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Correspondence to Ali Ahmadian or Mehdi Salimi.

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Communicated by Hui Liang.

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Amin, R., Ahmadian, A., Alreshidi, N.A. et al. Existence and computational results to Volterra–Fredholm integro-differential equations involving delay term. Comp. Appl. Math. 40, 276 (2021). https://doi.org/10.1007/s40314-021-01643-y

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  • DOI: https://doi.org/10.1007/s40314-021-01643-y

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