New Computational Algorithms for Analyzing the Stability of the Differential Equations System

In this paper we show how to improve the approximate solution of the large Lyapunov equation obtained by an arbitrary method. Moreover, we propose a new method based on refinement process and Weighted Arnoldi algorithm for solving large Lyapunov matrix equation. Finally, some numerical results will be reported to illustrate the efficiency of the proposed method

Stability Analysis of Distributed Order Fractional Differential Equations

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure

Application of Homotopy Perturbation Method for Fuzzy Linear Systems and Comparison with Adomian’s Decomposition Method

We present an efficient numerical algorithm for solution of the fuzzy linear systems (FLS) based on He’s homotopy perturbation method (HPM). Moreover, the convergence properties of the proposed method have been analyzed and also comparisons are made between Adomian’s decomposition method (ADM) and the proposed method. The results reveal that our method is effective and simple

A New Algorithm for Solving Large-Scale Generalized Eigenvalue Problem Based on Projection Methods

In this paper, we consider four methods for determining certain eigenvalues and corresponding eigenvectors of large-scale generalized eigenvalue problems which are located in a certain region. In these methods, a small pencil that contains only the desired eigenvalue is derived using moments that have obtained via numerical integration. Our purpose is to improve the numerical stability of the moment-based method and compare its stability with three other methods. Numerical examples show that the block version of the moment-based (SS) method with the Rayleigh–Ritz procedure has higher numerical stability than respect to other methods

An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence Analysis

In this paper, the Crank–Nicolson (CN) and rotated four-point fractional explicit decoupled group (EDG) methods are introduced to solve the two-dimensional time–fractional Burgers’ equation. The EDG method is derived by the Taylor expansion and 45° rotation of the Crank–Nicolson method around the x and y axes. The local truncation error of CN and EDG is presented. Also, the stability and convergence of the proposed methods are proved. Some numerical experiments are performed to show the efficiency of the presented methods in terms of accuracy and CPU time