广义基本解方法求解具有一类特殊热源的热传导方程反边界值问题

An Extended Method of Fundamental Solutions to the Problems of Inverse Boundary Value of the Heat-conduction Equation Involving One Specific Type of Heat Source

给出一种求解具有一类特殊热源的非齐次热传导方程反边界值问题的无网格方法,即广义基本解方法.该方法将问题的解分成特解和相应齐次问题的解两个部分:齐次解用基本解方法求解,而特解则是利用源项的特殊性由相应的特征方程的基本解近似得到.最后给出数值例子说明该方法的稳定性和有效性.

A meshless method, the extended method of fundamental solutions, is proposed to solve inverse boundary value problems for nonhomogeneous heat conduction involving one specific type of heat source. In the method, the solution is split into two parts, the particular and homogenous solutions. The homogenous solution is evaluated by the method of fundamental solutions, while an approximation of the particular solution is derived by using the fundamental solutions of the associated eigenvalue equations obtained due to the type - specificity of heat source. Numerical results are presented to verify the reliability and efficacy of the proposed method.