A new computational method for solution of non-linear Volterra–Fredholm integro-differential equations

Abstract

An approximation method is developed for the solution of high-order non-linear Volterra–Fredholm integro-differential (NVFID) equations under the mixed conditions. The approach is based on the orthogonal Chebyshev polynomials. The operational matrices of integration and product together with the derivative operational matrix are presented and are utilized to reduce the computation of Volterra–Fredholm integro-differential equations to a system of non-linear algebraic equations. Numerical examples illustrate the pertinent features of the method.

Keywords:

• non-linear equation
• integro-differential equation
• Chebyshev polynomials
• operational matrix
• Newton's method

2000 AMS Subject Classification :

• 45J05
• 42C10
• 65L60