二维对流反应扩散方程反问题的数值算法

Numerical Method of an Inverse Problem for Two-Dimensional Advection-Dispersion-Reaction Equations

讨论了一类二维对流反应扩散方程反问题的数值解法。应用拟解法的思想,把原问题分解为一系列适定的正问题和一个不适定的线性代数方程组。对于相应的正问题,证明了解连续依赖于初始分布,由此得到了在t时刻的稳定性估计。用古典欧拉差分格式求解正问题,用截断奇异值分解法求解病态方程组。数值结果显示数值解与理论解吻合良好。

The numerical method for the inverse problem of second-dimensional advection-dispersion- reaction equations is discussed in the article. By means of idea of the Quasi-Solution the inverse problem is converted into a sequence of well-posed forward problems and an ill-posed system of algebraic equations. For the corresponding forward problem, it gives the continuous dependence of the solution on the initial data, from which a stability estimate on time is obtained. The classic difference scheme of Euler is employed to solve the forward problem, and the truncated singular value decomposition is used to solve the ill-conditioned system of algebraic equation. The numerical simulation manifests that the numerical solution approaches the theoretical solution very well.