New methods for solving of nonlinear weakly singular integral equations

K. Maleknejad (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran)
H. Mesgarani (Faculty of Science, Shahid Rajaee University, Lavizan, Tehran, Iran)


ISSN: 0368-492X

Publication date: 1 June 2006



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


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.


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.


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



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

Download as .RIS



Emerald Group Publishing Limited

Copyright © 2006, Emerald Group Publishing Limited

Please note you might not have access to this content

You may be able to access this content by login via Shibboleth, Open Athens or with your Emerald account.
If you would like to contact us about accessing this content, click the button and fill out the form.
To rent this content from Deepdyve, please click the button.