A study on the convergence and error bound of solutions to 2D mixed Volterra–Fredholm integral and integro-differential equations via high-order collocation method

Document Type : Research Article

Authors

• A.A. Shalangwa ¹
• M.R. Odekunle ²
• S.O. Adee ²

¹ Department of Mathematical science, Gombe State University, Nigeria

² Department of Mathematics, Modibbo Adama University Yola, Nigeria.

10.22067/ijnao.2025.90535.1544

Abstract

The integral equation is transformed into systems of algebraic equations using standard collocation points, and then the algebraic equations are solved using matrix inversion. Their solutions are substituted into the approximate equation to give the numerical results. We establish the analysis of the developed method, which shows that the solution is unique, convergent, and error bound. To illustrate the effectiveness, ease of use, and dependability of the approach, illustrative examples are provided. It demonstrates that the method outperforms other methods.

Keywords

• Volterra integral equation
• Fredholm integral equation
• Mixed Volterra–Fredholm integral equation
• Collocation
• Two-dimensional integral

Main Subjects

• Computational Mathematics

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