in this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. in additional, the least-squares method is adopted tond the solution. to regularize the resultant ill-conditioned linear system ofequations, we apply the tikhonov regularization method to obtain the stablenumerical approximation to the solution. some numerical experiments con-rm the utility of...

We consider a local regularization method for the solution of first-kind Volterra integral equations with convolution kernel. The local regularization is based on a splitting of the original Volterra operator into “local” and “global” parts, and a use of Tikhonov regularization to stabilize the inversion of the local operator only. The regularization parameters for the local procedure include t...

In this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method cite{35} and the spectral method. The method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numer...

The topic of this thesis is the solution of integral equations in reproducing kernel Hilbert spaces. Special emphasis is put on the efficient exploitation of the space structure by a semi-discrete modelling. Firstly, a Tikhonov-Phillips method is considered and Sobolev error estimates as well as parameter strategies are established for various noise models. A modification of the objective funct...

Received () Revised () We propose a novel method for a solution of a system of linear equations with the non-negativity condition. The method is based on the Tikhonov functional and has better accuracy and stability than other well-known algorithms.

The O2 A-band night glow can be used to retrieve the temperature in range of 80–120 km mesosphere and lower thermosphere (MLT). From full spectrum glow, band is selected based on sensitivity emission line temperature, taking into account compromise relationship between spectral resolution, inversion efficiency, accuracy. non-linear iterative method optimization theory adopted for retrieval temp...