关于t^a型热传导方程解的定性研究及数值模拟

Qualitative Study and Numerical Simulation of the Solution of t^a Heat Conduction Equation

本文主要研究ta型热传导方程。从ta型热传导方程的导出入手,运用分离变量法求解此方程,得到ta型热传导方程的通解。其次,利用ta型热传导方程的边界条件以及初值条件,对其解的存在性、唯一性和稳定性进行了研究。最后,利用Matlab编程和有限差分法对热传导方程的解进行数值模拟,并讨论时间的幂次对热传导方程数值解的影响。

This paper is to study the heat conduction equation related to ta.First,we start from the origin of the heat conduction equation.The general solution of the heat conduction equation is obtained by using the separation of variables method.Secondly,we study the existence,uniqueness and stabil-ity of the solution of ta heat conduction equation under three boundary conditions.Finally,Matlab programming and finite difference method are used to simulate the solution of the heat conduction equation.And the influence of the power of time and the numerical solution of the heat conduction equation is discussed.