Green's function-based integral approaches to nonlinear transient boundary-value problems(II)

摘要

Two Green's function-based numerical formulations are used to solve the time-dependent nonlinear heat conduction (diffusion0 equation. These formulations, which are an extension of the first paper, utilize two fundamental solutions and the Green's second identity to achieve integral replications of the governing partial differential equation. The integral equations thus derived are discredited in space and time and aggregated in a finite element sense to give a system of nonlinear discrete equations that are solved by the Newton-Raphson algorithm. The mathematical simplicity of the Green's function of the first formulation facilitates its numerical implementation. The performance of the formulations is assessed by comparing their results with available numerical and analytical solutions. In all cases satisfactory and physicall7y realistic results are obtained.