一类特殊热传导时间反向问题的求解方法

A Method of Fundamental Solutions for the Backward Heat Conduction Problem Involving One Specific Type of Heat Source

针对具有一类特殊热源的非齐次热传导方程,给出一种求解其时间反向问题的无网格方法,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方程的特征函数近似得到.并用多个算例证明了该方法的稳定性和有效性.

A new meshless method is proposed to solve the backward heat conduction problem 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 eigenfunctions of the associated equations obtained due to the type-specificity of heat soure.Numerical results are presented to verify the reliability and efficacy of the proposed method.