Numerical solution of integral equations by using combination of Spline-collocation method and Lagrange interpolation

摘要

In this paper, we find numerical solution ofx(t)+λ∫abk(t,s)x(s)ds=y(t),a⩽t⩽borx(t)+λ∫atk(t,s)x(s)ds=y(t),a⩽t⩽b,a⩽s⩽bby B-Splines. We determined coefficients {αi}i=0N+1 such that∑i=0N+1αiBi(t)to be an approximation for x(t).This method give an approximate solution for integral equation, and also it is powerful in solving both Fredholm and Volterra integral equations, specially for the first kind. In this paper, we use special interpolation and quadrature rule for numerical integration.