Collocation method for Fredholm and Volterra integral equations

Abstract

Purpose

The purpose of this paper is to develop a numerical method based on quintic B‐spline to solve the linear and nonlinear Fredholm and Volterra integral equations.

Design/methodology/approach

The solution is collocated by quintic B‐spline and then the integral equation is approximated by the Gauss‐Kronrod‐Legendre quadrature formula.

Findings

The arising system of linear or nonlinear algebraic equations can solve the linear combination coefficients appearing in the representation of the solution in spline basic functions.

Practical implications

The error analysis of proposed numerical method is studied theoretically. Numerical results are given to illustrate the efficiency of the proposed method. The results are compared with the results obtained by other methods to verify that this method is accurate and efficient.

Originality/value

The paper provides new method to solve the linear and nonlinear Fredholm and Volterra integral equations.

Citation

Rashidinia, J. and Mahmoodi, Z. (2013), "Collocation method for Fredholm and Volterra integral equations", Kybernetes, Vol. 42 No. 3, pp. 400-412. https://doi.org/10.1108/03684921311323653