Search

To obtain the solution of nonlinear sequential fractional differential equations for Caputo operator two methods namely the Adomian decomposition method and Daftardar-Gejji and Jafari iterative method are applied in this paper. Finally some examples are presented to illustrate the efficiency of these methods. [ABSTRACT FROM AUTHOR]

This paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. Recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the Accelerated Overrelaxation (AOR) method. In this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditions. More precisely, it is demonstrated that the preconditioned Mixed-Type Splitting (MTS) iterative methods can surpass the preconditioned AOR iterative methods for an entirely general class of preconditioners handled by Wang and Song [J. Comput. Appl. Math. 226 (2009), no. 1, 114-124]. Finally some numerical results are elaborated which confirm the validity of the established results. [ABSTRACT FROM AUTHOR]

Solving large sparse linear systems is essential in numerous scientific domains. Several algorithms, based on direct or iterative methods, have been developed for parallel architectures. On distributed grids consisting of processors located in distant geographical sites, their performance may be unsatisfactory because they suffer from too many synchronizations and communications. The GREMLINS code has been developed for solving large sparse linear systems on distributed grids. It implements the multisplitting method that consists in splitting the original linear system into several subsystems that can be solved independently. In this paper, the performance of the GREMLINS code obtained with several libraries for solving the linear subsystems is analyzed. Its performance is also compared with that of the widely used PETSc library that enables one to develop portable parallel applications. Numerical experiments have been carried out both on local clusters and on distributed grids. [ABSTRACT FROM AUTHOR]

For solving nonlinear and transcendental equation f(x)=0, a singnificant improvement on Newton's method is proposed in this paper. New “Newton Like” methods are founded on the basis of Liapunov's methods of dynamic system. These new methods preserve quadratic convergence and computational efficiency of Newton's method, and remove the monotoneity condition imposed on f(x):f'(x)≠0 [ABSTRACT FROM AUTHOR]

In this paper, by applying Kronecker product and vectorization operator, we extend two mathematical equivalent forms of the conjugate residual squared (CRS) method to solve the periodic Sylvester matrix equation AjXjBj+CjXj+1Dj=Ejfor j=1,2,...,λ. We give some numerical examples to compare the accuracy and efficiency of the matrix CRS iterative methods with other methods in the literature. Numerical results validate that the proposed methods are superior to some existing methods and that equivalent mathematical methods can show different numerical performance. [ABSTRACT FROM AUTHOR]

We describe a new two-step iterative method for solving the absolute value equations Ax−|x|=b, which is an NP-hard problem. This method is globally convergent under suitable assumptions. Numerical examples are given to demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]