一类变系数抛物型方程的数值解法

Numerical solutions for a kind of variable coefficient parabolic differential equation

讨论了带有初边值条件的抛物型方程。该问题需要求解u(x,t)和未知变系数a(t)>0。这是一个反问题。利用有限差分方法给出了该问题的三层线性化差分格式。收敛阶在L∞范数下为O(h2+τ2)。在pc机上利用Matlab软件编程,计算数值算例验证了理论收敛阶。

The parabolic differential equation with initial and boundary conditions is discussed which needs to solve the function u（x,t） and an unknown positive coefficient a（t）.It is an inverse problem.The three-level linear difference format is presented with finite different method,and the convergence order in L∞ norm is O（h2＋τ2）.Numerical example in Matlab verify the theoretical result.