مجله بین المللی محاسبات و مدل سازی ریاضی
سال یکم شماره 2 (Spring 2011)

In this paper, we apply the compare the collocation methods of meshfree RBF over differential equation containing partial derivation of one dimension time dependent with a compound boundary nonlocal condition.

The coast of Bangladesh has a specialty in terms of high bending and many off- shore islands. Incorporation of the coastline and island boundaries properly in the numerical scheme is essential for accurate estimation of water levels due to surge. For that purpose a numerical scheme consisting of very fine mesh is required along the coastal belt, whereas this is unnecessary away from the coast. In this study, a fine mesh scheme covering the coastal belt and islands has been nested into a coarse mesh scheme covering up to 15 N latitude in the Bay of Bengal. For the existence of so many small and big islands and also for high bending of the coastline along the Meghna estuary, a very fine mesh scheme for the region between Barisal and Chittagong is again nested into the fine mesh scheme. A vertically integrated model is developed in Cartesian coordinate system to solve the shallow water equations using semi- implicit finite difference technique for computing surge associated with storms. The developedsystem is applied on a severe cyclonic storm ’SIDR’ that hit Bangladesh on 15th November, 2007. The computed water levels are found to be in good agreement with those observed.

Human language, over its evolutionary history, has emerged as one of the fundamental defining characteristic of the modern man. However, this milestone evolutionary process through natural selection has not left any ’linguistic fossils’ that may enable us to trace back the actual course of development of language and its establishment in human societies. Lacking analytical tools to fathom the critical essentials of evolutionary mechanism of cultural transmission, we seek the recourse of simulation study as another useful method of enquiry into the evolutionary trajectory of language. In this paper we use a toy model to understand an interesting feature of language evolution, namely, the scenario in which words gets fixed in a population of language users. We obtain simulation for the replicator dynamics that characterise the time rate of change of various words in the given language, using genetic algorithm to simulate the dynamics. We infer that two of the prime determinants for the establishment of a word within a linguistic population are its consonance with the grammar and its communicative efficiency.

In this paper, we consider the variational homotopy perturbation method (VHPM) to obtain an approximate series solution for the generalized Fisher’s equation which converges to the exact solution in the region of convergence. Comparisons are made among the variational iteration method (VIM), the exact solutions and the proposed method. The results reveal that the proposed method is very effective and simple and can be applied for other nonlinear problems in mathematical.

In this paper, we apply the Newton’s and He’s iteration formulas in order to solve the nonlinear algebraic equations. In this case, we use the stochastic arithmetic and the CESTAC method to validate the results. We show that the He’s iteration formula is more reliable than the Newton’s iteration formula by using the CADNA library.

In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

Fusion frames are an extension to frames that provide a framework for applications and providing efficient and robust information processing algorithms. In this article we study the erasure of subspaces of a fusion frame.

We present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. Numerical method of sixth-order with end conditions of the order 6 is derived. The convergence analysis of the method has been discussed. Numerical examples are presented to illustrate the applications of method, and to compare the computedresults with other known methods.