Improved Tikhonov Regularization Method For Source Term Inversion Of Fractional Order Alanomalous Diffusion Equation

Environmental pollution problems gradually coming into sight and has become the focus of our attention.It is eager to solve the current problem is that the accuracy issue of air pollution and ecological modeling marine water quality change. In the process,inversion of the pollution of the river which has become the goal of many research scholars.In the usual anomalous diffusion phenomenon, it is the most common example to search the river pollution sources. Because in the process of contaminant migration involved in time and space correlation issue,so by fractional anomalous diffusion equation to express the movement.The work of this paper is mainly analysis the advantages and shortcomings of Tikhonov regularization method, on the basis of classic Tikhonov regularization algorithm put forward an improved Tikhonov regularization method and analyzes the difference of the two algorithm.In order to verify the validity of the method,under the different disturbance, using the Tikhonov regularization method and the modified Tikhonov regularization method to solve the Fredholm integral equation respectively. Through the comparison of true solution and numerical solution, we can gain the modified Tikhonov regularization has higher accuracy in terms of equation than Tikhonov regularization.At the end of the paper, the fractional anomalous diffusion equation is calculated to use the forward modeling of implicit difference scheme.On the basis of forward modeling,we can obtain the fitting effect of numerical solution and the true solution by the modified Tikhonov regularization. The results of contrast and analysis showing that the modified Tikhonov regularization algorithm has higher convergence than the Tikhonov regularization, reach the desired goal.