TITLE:
Cubic Spline Approximation for Weakly Singular Integral Models
AUTHORS:
Franca Caliò, Elena Marchetti
KEYWORDS:
Volterra-Fredholm Integral Equations; Collocation Methods; Splines
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.11,
November
5,
2013
ABSTRACT: In this paper we propose a numerical collocation method to approximate the solution of linear integral mixed Volterra Fredholm equations of the second kind, with particular weakly singular kernels. The collocation method is based on the class of quasi-interpolatory splines on locally uniform mesh. These approximating functions are particularly suitable to tackle on problems with weakly regular solutions. We analyse the convergence problems and we present some numerical results and comparisons to confirm the efficiency of the numerical model.