TITLE:
The Numerical Solutions of Systems of Nonlinear Integral Equations with the Spline Functions
AUTHORS:
Xiaoyan Liu, Yurong Pan
KEYWORDS:
System of Integral Equations, Nonlinear Integral Equations, Numerical Solutions, Spline Functions
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.3,
March
12,
2020
ABSTRACT: The main goal of this work is to develop an effective technique for solving nonlinear systems of Volterra integral equations. The main tools are the cardinal spline functions on small compact supports. We solve a system of algebra equations to approximate the solution of the system of integral equations. Since the matrix for the algebraic system is nearly triangular, It is relatively painless to solve for the unknowns and an approximation of the original solution with high precision is accomplished. In order to enhance the accuracy, several cardinal splines are employed in the paper. Our schemes were compared with other techniques proposed in recent papers and the advantage of our method was exhibited with several numerical examples.