Non polynomial splines and weakly singular two-point boundary value problems (Q1116300)

The paper deals with an application of simple non-polynomial splines for solving numerically a weakly singular two-point boundary value problem. The authors prove that their collocation method is of the second order and gives a continuously differentiable approximation. As illustration two examples are presented and compared with the methods of \textit{M. Chawla} and \textit{C. Katti} [SIAM J. Numer. Anal. 22, 561-565 (1985; Zbl 0578.65085)], \textit{M. Chawla}, \textit{S. McKee} and \textit{G. Shaw} [BIT 26, 318-326 (1986; Zbl 0602.65063)] and \textit{S. R. K. Iyengar} and \textit{P. Jain} [Nume. Math. 50, 363-376 (1987; Zbl 0642.65062)]. It appears that the presented method yields better approximations of the exact solution.