Numerical solution of mixed Volterra-Fredholm integral equations using iterative method via two-variables Bernstein polynomials

• Main Authors: Farkhondeh Hosseini Shekarabi, Reza Ezzati
• Format: Article
• Language: English
• Published: Universidad Simón Bolívar 2018-09-01
• Series: Bulletin of Computational Applied Mathematics
• Subjects: Two-variable Bernstein polynomials; Mixed Volterra-Fredholm integral equations; Iterative method
• Online Access: https://drive.google.com/open?id=16auHframsKBPdN2Bh0Z2GLR9tMSieSV7

This paper is concerned with the numerical solution of mixed Volterra-Fredholm integral equations, based on iterative method and two variable Bernstein polynomials. In the main result, this method has several benefits in proposing an efficient and simple scheme with good degree of accuracy. Our second main result is to prove the convergence of the method, and to derive an upper bound under assumptions. Numerical experiments are performed for the approximation of the solution of two examples to demonstrate the accuracy and integrity of the method.