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

Articles in Press

Document Type : Research Article

Authors

• Ayuba Albert Shalangwa ¹
• M. R. Odekunle ²
• S. O. Adee ²

¹ Department of Mathematical Science, Gombe State University, Tudun-Wada Gombe, Nigeria.

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

10.22067/ijnao.2025.90535.1544

Abstract

In this research, we developed a polynomial collocation method for the solution of two-dimensional mixed Volterra-Fredholm integral and integro-differential equations. The Integral equation was transform into systems of algebraic equations using standard collocation points and then solve the algebraic equations using matrix inversion, their solutions are substituted into the approximate equation to give the numerical results. The analysis of the developed method was investigated and the solution was found to be 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 the other methods.

Keywords

• Volterra Integral equation
• Fredholm Integral equation
• Mixed Volterra-Fredholm Integral equation
• Collocation
• Two-Dimensional Integral

Main Subjects

• Computational Mathematics

---