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Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method

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Listed:
  • Mohamed R. Ali
  • Mohamed M. Mousa
  • Wen-Xiu Ma

Abstract

We present a new numerical technique to discover a new solution of Singular Nonlinear Volterra Integral Equations (SNVIE). The considered technique utilizes the Hybrid Orthonormal Bernstein and Block‐Pulse functions wavelet method (HOBW) to solve the weakly SNVIE including Abel’s equations. We acquire the HOBW implementation matrix of the integration to derive the procedure of solving these kind integral equations. The explained technique is delineated with two numerical cases to demonstrate the benefit of the technique used by us. At last, the exchange uncovers the way that the strategy utilized here is basic in usage.

Suggested Citation

  • Mohamed R. Ali & Mohamed M. Mousa & Wen-Xiu Ma, 2019. "Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2019(1).
    • Handle: RePEc:wly:jnlamp:v:2019:y:2019:i:1:n:1705651
    DOI: 10.1155/2019/1705651
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    References listed on IDEAS

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    1. Zhu, Li & Wang, Yanxin, 2015. "Numerical solutions of Volterra integral equation with weakly singular kernel using SCW method," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 63-70.
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    Cited by:

    1. Abeer M. Al-Bugami & M. A. Abdou, 2025. "An Algorithm for Solving Phase‐Lag Nonlinear Mixed Integral Equation With Discontinuous Generalized Kernel," Advances in Mathematical Physics, John Wiley & Sons, vol. 2025(1).

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