An efficient computational method for modelling transient heat conduction with nonlinear source terms (Q1922276)

We propose an efficient method, the Laplace transform dual reciprocity method (LTDRM), for solving the title problem. Due to the nonlinearity, the source terms are linearized first, followed by a Laplace transform performed to the linearized differential system. The unknowns are then found in the transformed space by the dual reciprocity method, after which their values in physical space are obtained through a numerical inversion. As examples we used the LTDRM to solve microwave heating and spontaneous ignition problems.