Ashyralyyev, Charyyar; Dedeturk, Mutlu

A finite difference method for the approximate solution of the inverse problem for the multidimensional elliptic equation with overdetermination is applied. Stability and coercive stability estimates of the first and second orders of accuracy difference schemes for this problem are established. The algorithm for approximate solution is tested in a two-dimensional inverse problem.

Ashyralyyev, Charyyar; Demirdag, Oznur

The boundary value problem of determining the parameter p of a parabolic equation ′(t)+A(t)=f(t)+p(0≤t≤1),(0)=,(1)= in an arbitrary Banach space E with the strongly positive operator A is considered. The first order of accuracy stable difference scheme for the approximate solution of this problem is investigated. The well-posedness of this difference scheme is established. Applying the abstract result, the stability and almost coercive stability estimates for the solution of difference schemes for the approximate solution of differential equations with parameter are obtained.

Ashyralyyev, Charyyar; Dural, Ayfer; Sozen, Yasar

A finite difference method for the approximate solution of the reverse multidimensional parabolic differential equation with a multipoint boundary condition and Dirichlet condition is applied. Stability, almost coercive stability, and coercive stability estimates for the solution of the first and second orders of accuracy difference schemes are obtained. The theoretical statements are supported by the numerical example.

Cakir, Zafer

The stable difference schemes for the fractional parabolic equation with Dirichlet and Neumann boundary conditions are presented. Stability estimates and almost coercive stability estimates with ln (1 / ( + | h |)) for the solution of these difference schemes are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes of one-dimensional fractional parabolic partial differential equations.

Merdan, Mehmet; Gökdogan, Ahmet; Yildirim, Ahmet; Mohyud-Din, Syed Tauseef

An approximate analytical solution of fractional Fornberg-Whitham equation was obtained with the help of the two-dimensional differential transformation method (DTM). It is indicated that the solutions obtained by the two-dimensional DTM are reliable and present an effective method for strongly nonlinear partial equations. Exact solutions can also be obtained from the known forms of the series solutions.