TITLE:
Solving Systems of Volterra Integral Equations with Cardinal Splines
AUTHORS:
Xiaoyan Liu, Zhi Liu, Jin Xie
KEYWORDS:
Spline Functions, Integral Equations, Numerical Methods
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.11,
November
23,
2015
ABSTRACT: This work is a continuation of the earlier article [1]. We establish new numerical methods for solving systems of Volterra integral equations with cardinal splines. The unknown functions are expressed as a linear combination of horizontal translations of certain cardinal spline functions with small compact supports. Then a simple system of equations on the coefficients is acquired for the system of integral equations. It is relatively straight forward to solve the system of unknowns and an approximation of the original solution with high accuracy is achieved. Several cardinal splines are applied in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined and the convergence rate is investigated. We demonstrated the value of the methods using several examples.