We present a new numerical approach to solving the fractional differential Riccati equations numerically. The approach—called Mittag-Leffler–Galerkin method—comprises finite Mittag-Leffler function and Galerkin method. error analysis of method was studied. As result, we two theorems by which can be bounded. In addition analysis, residual correction method, allows us estimate obtain approximate ...

The embedded discontinuous Galerkin methods are obtained from hybridizable discontinuous Galerkin methods by a simple change of the space of the hybrid unknown. In this paper, we consider embedded methods for second-order elliptic problems obtained from hybridizable discontinuous methods by changing the space of the hybrid unknown from discontinuous to continuous functions. This change results ...

In the present study, a fractional order differential equation with deviating argument is considered in a separable Hilbert space H . We will prove the existence and convergence of an approximate solution for the given problem by using the analytic semigroup theory and the fixed point method. Finally, we consider the Faedo-Galerkin approximation of the solution and prove some convergence results.

We unify the formulation and analysis of Galerkin and Runge–Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximate solutions, allows us to establish a posteriori superconvergence estimates for the error at the nodes for all methods.

This paper introduces a numerical method to solve anti-periodic boundary value problems. The proposed method converts anti-periodic boundary value problem to a Fredholm integral equation and solves it by Galerkin method. The approximate solution converges to the exact solution and satisfies anti-periodic boundary conditions completely. Also, the convergence rate of the proposed method is given ...

The existence, uniqueness approximate solutions of a stochastic fractional differential equation with deviating argument is studied. Analytic semigroup theory and fixed point method is used to prove our results. Then we considered Faedo-Galerkin approximation of solution and proved some convergence results. We also studied an example to illustrate our result.

The purpose of this paper is to approximate the solution of a Cauchy integral equation of the second kind, using projection, finite rank approximations and a regularization procedure. We us the Kantorovich projection, the Sloan projection, the Galerkin projection, respectively. We give a general framework and we prove the existence of the solution for a projection schemes. 2012 Elsevier Inc. Al...

EEorts to develop sinc domain decomposition methods for second-order two-point boundary-value problems have been successful, thus warranting further development of these methods. A logical rst step is to thoroughly investigate the extension of these methods to Poisson's equation posed on a rectangle. The Sinc-Galerkin and sinc-collocation methods are, for appropriate weight choices, identical f...