二维变系数抛物型方程参数反演的摄动量算法

Parameter Inversion for Two-Dimensional Parabolic Equation with Variable Coefficients Using the Best-Disturbed Numerical Method

讨论了二维变系数抛物型方程的参数识别反问题,将其归为最优化问题,应用基于正则化方法的反问题求解方法—最佳摄动量法,给出数值求解。并利用此方法反演计算了具有分段函数系数的二维抛物型方程的参数识别反问题,通过对具体算例的程序实现和数值计算,验证了最佳摄动量法解决此类问题的有效性和可行性。

For the inverse problem respect to parameter inversion of two_dimensional parabobic equation with variable coefficients, the paper transformed the inverse problem to the optimized problem of operator theory, the best_disturbed iteration numerical methods that based on the regularization method are used for solving the inverse problem,and gave the numerical solution. The method is successfully put into practice to solving the inverse problem of two_dimensional parabobic equation whose coefficient is partition paragraph function,it turns out that the best perturbation method is one of the efficient methods to solve this kind of problems.