An Extension of the LTDRM to Some Highly Nonlinear Diffusion Equations

Abstract

The boundary element method (BEM) is a very attractive numerical approach in science and engineering due to its accuracy and efficiency. However, the attractiveness of the BEM is somehow devalued when it is used to solve diffusion problems with source terms, since singular domain integrals usually appear in a BEM formulation. One of the solutions, among many others, is to adopt the so-called dual reciprocity method (DRM) combined with a time-marching scheme as demonstrated in Zhu et al. [1]. On the other hand, time-marching schemes can be quite time consuming, especially when a nonlinear iteration must be carried out at each time step for a nonlinear problem. Recently, Zhu et al. [2] showed an alternative to time-marching schemes; they combined DRM with the Laplace transform, which they called the Laplace transform dual reciprocity method (LTDRM). As a problem is solved in the Laplace space by the DRM before the final solution in time domain is obtained through an inverse Laplace transform, a clear advantage of the LTDRM over time-stepping methods were demonstrated through their numerical examples.