Let {ak}, k = 1, . . . , N be a family of matrices of sizes rk × rk−1. For positive integers i, j, i > j define the operation aij as follows: a × ij = ai−1 · · ·aj+1 for i > j + 1, aj+1,j = Irj . Let {bk}, k = 1, . . . , N be a family of matrices of sizes rk−1 × rk. For positive integers i, j, j > i define the operation bij as follows: b × ij = bi+1 · · · bj−1 for j > i+ 1, bi,i+1 = Iri . It is...

Variational iteration method is applied to examine the temperature distribution within a single fin with a one-dimensional steady-state nonlinear heat conduction equation. Variation of temperature due to different levels of nonlinearities is analyzed. The results obtained by means of variational iteration method are compared with the results obtained from finite element method. A fourth iterati...

In this paper, the variational iteration method is used to solve the Cauchy problem. Some examples are given to elucidate the solution procedure and reliability of the obtained results. The variational iteration algorithm leads to exact solutions in the present study. © 2010 Elsevier Ltd. All rights reserved.

In this paper, we revisit the D-iteration algorithm in order to better explain different performance results that were observed for the numerical computation of the eigenvector associated to the PageRank score. We revisit here the practical computation cost based on the execution runtime compared to the theoretical number of iterations.

Abstract The basic requirement of Newtons method in solving systems of nonlinear equations is, the Jacobian must be non-singular. Violating this condition, i.e. the Jacobian to be singular the convergence is too slow and may even be lost. This condition restricts to some extent the application of Newton method. In this paper we suggest a new approach for solving fuzzy nonlinear equations where ...

In this paper, we report the application of two parameter coupled alternating group explicit (CAGE) iteration and Newton-CAGE iteration methods for the cubic spline solution of non-linear differential equation u" = f(r,u,u') subject to given natural boundary conditions. The error analysis for CAGE iteration method is discussed in details. We compared the results of proposed CAGE iteration metho...

This paper deals with computational algorithms for obtaining the optimal stationary policy and the minimum cost of a discounted semi-Markov decision process. Van Nunen [23) has proposed a modified policy iteration algorithm with a suboptimality test of MacQueen type, where the modified policy iteration algorithm is policy iteration method with the policy evaluation routine by a finite number of...