APPLICATION OF THE BESSEL-HYBRID FUNCTIONS FOR THE LINEAR FREDHOLM-VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

Abstract

In this paper a collocation method based on the Bessel-hybrid functions is used for approximation of the solution of linear Fredholm-Volterra integro-differential equations (FVIDEs) under mixed conditions. First, we explain the properties of Bessel-hybrid functions, which are combination of block-pulse functions and Bessel functions of first kind. The method is based upon Bessel-hybrid approximations, so that to obtain the operational matrixes and approximation of functions we use the transfer matrix from Bessel-hybrid functions to Taylor polynomials. The matrix equations correspond to a system of linear algebraic equations with the unknown Bessel-hybrid coefficients. Present results and comparisons demonstrate our estimate have good degree of accuracy.

Keywords

• Bessel-hybrid functions
• Integro-differential equations
• Collocation
• Fredholm
• Volterra