An application of the LTDRM to transient diffusion problems with nonlinear material properties and nonlinear boundary conditions

摘要

In this paper, we shall present an application of the Laplace Transform Dual Reciprocity Method (LTDRM) to the solution of transient diffusion problems with nonlinear material properties and nonlinear boundary conditions. Two methods, with and without utilizing the Kirchhoff transformation, will be discussed. The nonlinear terms in both governing equation and boundary conditions are linearized first followed by the removal of the time variable from the linearized differential system with the Laplace transformation, and then the problem is solved by the dual reciprocity method. As a result, a solution at any specific time can be obtained without step-by-step calculations in time domain and computations of domain integrals. To show the efficiency and accuracy of the present method, several problems are analyzed, and their solutions are compared with those obtained either analytically or numerically.