A variational approach to a BVP arising in the modelling of electrically conducting solids

Abstract

The purpose of this paper is to apply an amended variational scheme, based on an adapted domain decomposition, for the solution of a second-order nonlinear boundary value problem that arises in applications involving the diffusion of heat generated by positive temperature dependent sources. The underlying idea of this approach is to decompose the original interval prior to the implementation of the iterative variational approach in order to improve the accuracy and acquire uniform convergence to the exact solution over the entire domain. Convergence analysis is given and then numerical experiments are carried out to make obvious the convergence, accuracy and efficient applicability of the method.