مجله بین المللی محاسبات و مدل سازی ریاضی
سال هفتم شماره 3 (Summer 2017)

In this paper, we propose a technique for determining a source term in an inverse heat conduction problem (IHCP) using Radial Basis Functions (RBFs). Because of being very suitable instruments, the RBFs have been applied for solving Partial Dierential Equations (PDEs) by some researchers. In the current study, a stable meshless method will be pro- posed for solving an (IHCP). The other advantage of the method is that can be applied to the problems with various types of boundary conditions. The results of numerical experiments are presented and compared with analytical solutions. The results demonstrate the reliability and efficiency of the proposed scheme.

‎The ABS methods‎, ‎introduced by Abaffy‎, ‎Broyden and Spedicato‎, ‎are‎ ‎direct iteration methods for solving a linear system where the‎ ‎$i$-th iteration satisfies the first $i$ equations‎, ‎therefore a‎ ‎system of $m$ equations is solved in at most $m$ steps‎. ‎In this‎ ‎paper‎, ‎we introduce a class of ABS-type methods for solving a full row‎ ‎rank linear equations‎, ‎where the $i$-th iteration solves the first‎ ‎$3i$ equations‎. ‎We also extended this method for $k$ steps‎. ‎So‎, ‎termination is achieved in at most $left[frac{m+(k-1)}{k}right]$‎ ‎steps‎. ‎Morever in our new method in each iteration, we have the‎ ‎the general solution of each iteration‎.

‎In this paper‎, ‎we present a new modification of Newton's method‎ ‎for finding a simple root of a nonlinear equation‎. ‎It has been‎ ‎proved that the new method converges cubically‎.

‎In this work, we find the differential transforms of the functions $tan$ and‎ ‎$sec$‎, ‎and then we applied this transform on a class of partial differential equations involving $tan$ and‎ ‎$sec$‎.

‎In this work‎, ‎we consider the parabolic equation‎: ‎$u_t-u_{xx}=0$‎. ‎The purpose of this paper is to introduce the method of‎ ‎variational iteration method and radial basis functions for‎ ‎solving this equation‎. ‎Also, the method is implemented to three‎ ‎numerical examples‎. ‎The results reveal‎ ‎that the technique is very effective and simple.

In this paper, a theorem is proved which presents the series solution obtained from the homotopy analysis method is convergent to the exact solution of nonlinear age-structured population models.