Numerical solution of a free surface seepage problem from nonlinear channel

Abstract

We describe the numerical solution of a nonlinear Cauchy singular integral equation depending on an unknown parameter and referring to a free boundary value problem of free surface from a channel. We propose a Newton collocation method and discuss various computational aspects in order to obtain an effective algorithm. Numerical results are presented.

Keywords:

• nonlinear Cauchy singular integral equation
• quadrature method
• Newton iteration method
• fast algorithm