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

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 بهمن 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.90535.1544

نویسندگان

Ayuba Albert Shalangwa^{* 1}؛ M. R. Odekunle²؛ S. O. Adee²

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

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

چکیده

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.

کلیدواژه‌ها

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