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A Galerkin finite element method is constructed for computing solution of the Fisher equation. Hyperbolic-trigonometric tension (HTT) B-splines are used as weight and shape functions in the Galerkin approach. Fully discretization of the Fisher equation is fulfilled via Crank-Nicolson method in time and Galerkin method in space. Travelling wave front solution is studied to show robustness of the presented scheme on Fisher equation. The numerical results obtained with the present method are satisfactory with regard to its accuracy. [ABSTRACT FROM AUTHOR]

A numerical approach is defined to get the solution of the regularized long wave (RLW) equation. The hyperbolic- trigonometric tension (HTT) B-spline is adapted as a trial function to the Galerkin method. Space integration of the RLW equation is managed trough HTT B-spline Galerkin method over the finite elements. Resulting system of ordinary differential equations is integrated using the Crank Nicolson technique. Thus RLW equation is fully integrated into system of nonlinear algebraic equations. Solution of this system gives the approximate solution of the RLW equation over the given problem domain. [ABSTRACT FROM AUTHOR]

This paper proposes a stabilization method to approximate analytical solutions of magnetohydrodynamics (MHD) equations. The method adds two modular grad-div steps into fully-discrete finite element MHD solver. The main idea in these intrusive steps is to penalize the divergence of the velocity/magnetic fields both in L2 and H1-norms. The paper confirms the optimal convergence of the method, and gives numerical experiments which reveal positive effect of the method as in the usual grad-div stabilization. [ABSTRACT FROM AUTHOR]

In the present paper, a space-dependent identification problem for parabolic-elliptic equations is investigated. The second order of accuracy r-modified Crank-Nicholson difference schemes for the numerical solution of the source identification parabolic-elliptic problems are presented. Numerical results are given. [ABSTRACT FROM AUTHOR]

In the present paper, a source identification problem for elliptic-telegraph equation with non-local condition is studied. Stability estimates for the differential equations of the source identification problem are established. Furthermore, stability estimates for the difference schemes of the source identification problem are presented. [ABSTRACT FROM AUTHOR]

In the present paper, we study a source identification problem for hyperbolic-parabolic equation with nonlocal conditions. The stability estimates for the solution of this source identification problem are established. Furthermore, we construct the second order of accuracy difference scheme for the approximate solution of the problem under consideration. The stability estimates for the solution of this difference scheme are presented. [ABSTRACT FROM AUTHOR]

In the present paper, source identification problem for the telegraph equation is investigated. The first order of accuracy absolute stable difference scheme for the numerical solution of the one dimensional identification problem for the telegraph equation with the Dirichlet condition is presented. Some numerical results are provided. [ABSTRACT FROM AUTHOR]