Spline Collocation for Volterra - Fredholm Integro-Differential Equations Journal Article

A collocation procedure is developed for the linear and nonlinear Volterra - Fredholm integro-differential equations, using the globally defined B-spline and auxiliary basis functions. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically.

"Yalcinbas in [15] developed the Taylor polynomial solutions for the nonlinear Volterra-Fredholm integral equations and in [14] considered the high-order linear Volterra- We introduce the cubic B-spline space and basis functions to construct an interpolation s to be used in the formulation of the cubic B-spline collocation method. Conclusions In the present work, a technique has been developed for solving linear and nonlinear Volterra- Fredholm integro-differential equations by using the Newton-Cotes formula and collocating by cubic B-spline. , 2008 , New direct method to solve nonlinear Volterra-Fredholm integral and integro- differential equations using operational matrix with blockpulse functions,Progress In Electromagnetics Research B, vol. , 2009 , Numerical solution of nonlinear Volterra-Fredholm integro-differential equations via direct method using triangular functions,Computers and Mathematics with Applications, vol. , 2011, Hybrid Legendre polynomials and block-pulse functions approach for nonlinear Volterra- Fredholm integro-differential equations, Computers and Mathematics with Applications, vol."