On the application of multiquadric bases in conjunction with the LTDRM method to solve nonlinear diffusion equations

摘要

As transient diffusion equations with nonlinear source terms have broad engineering applications, many numerical solution approaches have been proposed in the past. One of the numerically efficient and accurate methods was the Laplace transform dual reciprocity method (LTDRM). As a result of a series of studies to further improve the accuracy and efficiency of the LTDRM, we shall present, in this paper, the LTDRM in conjunction with the multiquadric bases, which were shown to possess a better convergence rate than other interpolation functions such as linear interpolation functions or augmented thin plate splines (ATPS). Three test examples are included in this paper to support the previous theoretical work and to provide evidence that the multiquadric bases are indeed superior when they are used in conjunction with the LTDRM.