This article considers an inverse problem of time fractional parabolic partial differential equations with the nonlocal boundary condition. Dirichlet-measured output data are used to distinguish the unknown coefficient. A finite difference scheme is constructed and a numerical approximation is made. Examples and numerical experiments, such as man-made noise, are provided to show the stability and efficiency of this numerical method.

In this work the inverse cofficient problem for Euler-Bernoulli equation with periodic boundary and integral addition conditions is investigated. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown by using the generalized Fourier method. Numerical tests using the implicit finite difference scheme combined with an iterative method are presented and discussed. Also an example is presented with figures.

In this work, two-dimensional inverse quasi-linear parabolic problem with periodic boundary and integral overdetermination conditions is investigated. The formal solution is obtained by the Fourier approximation. Under some natural regularity and consistency conditions on the input data,the existence, uniqueness and continuously dependence upon the data of the solution are proved by iteration method. The inverse problem is first examined by linearization and then used implicit finite difference scheme for the numerical solution. Also predictor corrector method is considered in the numerical approach. Some results on the numerical solution with two examples are presented with figures and tables. The sensitivity of the scheme with respect to noisy overdetermination data is illustrated.

In this work, the inverse quasi-linear pseudo-parabolic problem was investigated. We demonstrated the solution by the Fourier approximation. The inverse problem was first examined by linearizing and then used implicit finite difference schema for the numerical solution.