A Stable And Fast Algorithm For Source Identification In Parabolic Equation

The source identification of Parabolic Equation as a active branch in inverse problems of differential equations, has important practical background, and it is ill-posed in sense of Hadamard, so it is difficult to get its stable numerical solutions, and it has attracted many researchers' interests in the solving settings.Based on the properties of nonnegative operator and well-known LaxMilgram theorem, this paper is devoted to transform the problem into a well-posed and second kind of Volterra equation, and to propose a new stable and fast algorithm. As to the determination of regularization parameter, the algorithm employs two posterior strategies in a new way, which can be numerically realized under the cases of with and without knowing the error level of input data. The numerical tests are made and shown that the method possesses widespread adaptability, good stability and it is much more faster than Tikhonov regularization.