On Solutions of Linear Functional Integral and Integro-Differential Equations via Lagrange Polynomials

Abstract

In this study, a matrix-collocation method is developed numerically to solve the linear Fredholm-Volterra-type functional integral and integro-differential equations. The linear functional integro-differential equations are considered under initial conditions. The mentioned type problems often appear in various branches of science and engineering such as physics, biology, mechanics, electronics. The method essentially is a collocation method based on the Lagrange polynomials and matrix operations. By using presented method, the problem is reduced to a system of linear algebraic equations. The solution of this system gives the coefficients of assumed solution. An error analysis based on the residual function is studied. Some examples are solved to demonstrate the accuracy and efficiency of the method.

A streamlined numerical method to treat fractional nonlinear terminal value problems with multiple delays appearing in biomathematics

“…The Lagrange interpolation polynomial solution form was previously established for the integral and integer order integro-differential equation (Yüzbaşı and Sezer 2021 ). In this study, we shall develop it in the solution form of FNTVPs ( 1 ) and the matrix relations, as where ’s are unknown Lagrange interpolation coefficients, which have to be determined, and denotes the Lagrange interpolation polynomial, which possesses an explicit form (see Abramowitz and Stegun 1964 ) such that represents the standard collocation points .…”