Regularization methods for identifying the initial value of time fractional pseudo-parabolic equation.

In this paper, the problem we investigate is that the inverse problem of identifying the initial value for fractional pseudo-parabolic equation. This problem is ill-posed, i.e. the solution (if exists) does not depend on the measurable data. We give the estimate of conditional stability under an a-priori bound assumption for exact solution. Two regularization methods are used to solve this problem, and under an a-priori and an a-posteriori selection rule for the regularization parameter, the error estimates for these methods are obtained. Finally, several numerical examples are given to prove the effectiveness of these regularization methods. [ABSTRACT FROM AUTHOR]