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In this paper, we propose a new splitting scheme for reformulation of the Vlasov Maxwell Fokker Planck (VMFP) system, which produces a new recursive algorithm for its solution. We demonstrate that this algorithm converges to a unique solution. Also, we obtain an a posteriori error estimation, in practical finite element analysis, for sub-problems of the recursive algorithm. The paper also contains brief comments on error estimations of solutions of the VMFP system, particularly when mixed methods are employed. Finally, a numerical example is provided to demonstrate the accuracy and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a new discontinuous finite element idea for the time fractional diffusion-wave equation defined in bounded domain. The time fractional derivatives are described in the Caputo's sense. By applying the sine transform on the time fractional diffusion-wave equation, we make the equation depend on time. Then we use definition of Caputo's derivative and by defining l-degree discontinuous finite element with interpolated coefficients we solve the mentioned equation. Error estimate, existence and uniqueness are proved. Finally, the theoretical results are tested by some numerical examples. [ABSTRACT FROM AUTHOR]

In this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. We prove a posteriori L2(L2) and error estimates for this method under minimal regularity hypothesis. Test problem of an applica- tion of the wave equation in the laser is presented to verify the efficiency and accuracy of the method. [ABSTRACT FROM AUTHOR]

We investigate the analytical and numerical solutions of the modified Kortweg de Vries equation by applying the idea of commutative hypercomplex mathematics, He's homotopy perturbation method as a simple particular procedure, and the Runge-Kutta discontinuous Galerkin methods. Moreover, we discuss at great length the convergence conditions for this equation by using the Banach fixed point theory, which could provide a good iteration algorithm. Finally, we compare the homotopy perturbation method with some standard ideas same as the Runge-Kutta discontinuous Galerkin method by some numerical illustrations. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the numerical solution of the general fractional partial differential equations. To this end, we introduce an efficient new basis based on the generalized fractional-order Bernstein functions. A general formulation for the fractional Bernstein operational matrix of fractional integral operator and derivatives operator for the first time is obtained. In this approach, a truncated fractional Bernstein series together with the fractional Bernstein operational matrix are used to reduce the such problems to those of solving a system of algebraic equations thus greatly simplifying the problem. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. Presented results show that the method will improve the solutions of fractional partial differential equations. [ABSTRACT FROM AUTHOR]

The generalized solitary solutions of the nonlinear coupled Klein-Gordon equation are obtained by using Exp-function method with free parameters. This method is introduced as a simple particular procedure for comparing the approximation solutions of Runge-Kutta discontinuous Galerkin (RKDG) methods and exact solutions. [ABSTRACT FROM AUTHOR]

In this paper, we apply the first integral method to study the exact solutions of different coupled nonlinear Maccari's systems [ABSTRACT FROM AUTHOR]