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September 10, 2025

Numerical Solution of Two Dimensional Mixed Volterra-Fredholm Integral Equations Using Polynomial Collocation Method

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Authors

ASAlbert A. ShalangwaMOM. R. OdekunleSASolomon O. Adee

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Overview

This research develops a numerical solution method for two-dimensional Volterra-Fredholm equations, demonstrating increased accuracy with larger N values.

Key Points

  • The polynomial collocation method effectively solves linear two-dimensional mixed Volterra-Fredholm integral equations.
  • Using Bernstein polynomials, the method transforms integral equations into algebraic systems, solved via Gaussian elimination.
  • Illustrative examples show the method converges faster to the exact solution as the value of N increases.
  • This approach highlights the efficiency and accuracy of solving complex integral equations in numerical analysis.

Cite This Study

Shalangwa et al. (2025) studied this question.

synapsesocial.com/papers/68c1a5eb54b1d3bfb60df75ehttps://doi.org/10.64290/bima.v9i1a.892
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Also Consider

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  1. 1A Numerical Method for the Solution of Linear Volterra Integral Equations2024
  2. 2Numerical treatment of linear Volterra integro differential equations using variational iteration algorithm with collocation2024 · 1 citations
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  4. 4Numerical Solution of Volterra's Integral Equations by Collocation and Taylor Method2024
  5. 5A Direct Polynomial Solution of Nonlinear Volterra-Fredholm Integro-Differential Equations via the Shifted Chebyshev Collocation Method2026