TY  - JOUR
AB  - 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.
VL  - 35
IS  - 5
SN  - 0368-492X
DO  - 10.1108/03684920610662511
UR  - https://doi.org/10.1108/03684920610662511
AU  - Maleknejad K.
AU  - Mesgarani H.
PY  - 2006
Y1  - 2006/01/01
TI  - New methods for solving of nonlinear weakly singular integral equations
T2  - Kybernetes
PB  - Emerald Group Publishing Limited
SP  - 753
EP  - 760
Y2  - 2024/05/08
ER  -