New methods for solving of nonlinear weakly singular integral equations

Abstract

Purpose

Aims to present a boundary integral equation method for solving Laplace's equation Δu=0 with nonlinear boundary conditions.

Design/methodology/approach

The nonlinear boundary value problem is reformulated as a nonlinear boundary integral equation, with u on the boundary as the solution being sought. The integral equation is solved numerically by using the collocation method on smooth or nonsmooth boundary; the singularities of solution degrade the rates of convergence.

Findings

Variants of the methods for finding numerical solutions are suggested. So these methods have been compared with respect to number of iterations.

Practical implications

Numerical experiments show the efficiency of the proposed methods.

Originality/value

Provides new methods to solve nonlinear weakly singular integral equations and discusses difficulties that arise in particular cases.

Citation

Maleknejad, K. and Mesgarani, H. (2006), "New methods for solving of nonlinear weakly singular integral equations", Kybernetes, Vol. 35 No. 5, pp. 753-760. https://doi.org/10.1108/03684920610662511