Collocation method for Fredholm and Volterra integral equations
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.
integral equations quintic b-spline linear and nonlinear fredholm and volterra integral equations gauss-kronrod-legendre quadrature formula error analysis mathematics