Numerical solutions for nonlinear Volterra-Fredholm integral equations of the second kind with a phase lag

Abstract

This study is focused on the numerical solutions of the nonlinear Volterra-Fredholm integral equations (NV-FIEs) of the second kind, which have several applications in physical mathematics and contact problems. Herein, we develop a new technique that combines the modified Adomian decomposition method and the quadrature (trapezoidal and Weddle) rules that used when the definite integral could be extremely difficult, for approximating the solutions of the NV-FIEs of second kind with a phase lag. Foremost, Picard's method and Banach's fixed point theorem are implemented to discuss the existence and uniqueness of the solution. Furthermore, numerical examples are presented to highlight the proposed method's effectiveness, wherein the results are displayed in group of tables and figures to illustrate the applicability of the theoretical results.

Keywords

• nonlinear volterra-fredholm integral equation
• picard's method
• banach's fixed point theorem
• modified adomian decomposition method
• trapezoidal and weddle's quadrature rules
• contact problems
• phase lag