The discrete collocation method for weakly singular Urysohn equations

Abstract

In this paper, we analyse the iterated collocation method for the nonlinear Urysohn operator equation x=y+K(x) with K a singular kernel. The paper extends the study [H. Kaneko, R.D. Noren, and P.A. Padilla, J. Comput. Appl. Math. 80 (1997), pp. 335–349] in which the convergence of the iterated collocation method for Urysohn equations is considered.

Keywords:

• the iterated collocation method
• the discrete collocation method
• Urysohn equation
• weakly singular equation
• spline projection

2000 AMS Subject Classification :

• 65L60
• 47D03
• 45G05

CCS Category :

• G.1.9
• G.1.4