IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION
Year:2015 | Volume:5 | Issue:1 |Papers Count:6

In this paper, a class of semi-implicit two-stage stochastic Runge-Kuttamethods (SRKs) of strong global order one, with minimum principal er-ror constants are given. These methods are applied to solve It^o stochas-tic di erential equations (SDEs) with a Wiener process. The e ciency ofthis method with respect to explicit two-stage It^o Runge-Kutta methods(IRKs), It^o method, Milstien method, semi-implicit and implicit two-stageStratonovich Runge-Kutta methods are demonstrated by presenting somenumerical results.

In this paper, a two-phase algorithm, namely IVNS, is proposed for solvingnonlinear optimal control problems. In each phase of the algorithm, we use avariable neighborhood search (VNS), which performs a uniform distributionin the shaking step and the successive quadratic programming, as the localsearch step. In the  rst phase, VNS starts with a completely random initialsolution of control input values. To increase the accuracy of the solutionobtained from the phase 1, some new time nodes are added and the valuesof the new control inputs are estimated by spline interpolation. Next, inthe second phase, VNS restarts by the solution constructed by the phase1. The proposed algorithm is implemented on more than 20 well-knownbenchmarks and real world problems, then the results are compared withsome recently proposed algorithms. The numerical results show that IVNScan  nd the best solution on 84% of test problems. Also, to compare theIVNS with a common VNS (when the number of time nodes is same in bothphases), a computational study is done. This study shows that IVNS needsless computational time with respect to common VNS, when the quality ofsolutions are not di erent signi cantly.

In this paper, the sinc collocation method is proposed for solving linearand nonlinear multi-order fractional di erential equations based on the newde nition of fractional derivative which is recently presented by Khalil, R., Al Horani, M., Yousef, A. and Sababeh, M. in A new de nition of fractionalderivative, J. Comput. Appl. Math. 264 (2014), 65{70. The propertiesof sinc functions are used to reduce the fractional di erential equation to asystem of algebraic equations. Several numerical examples are provided toillustrate the accuracy and e ectiveness of the presented method.

We introduce a RBFs mesheless method of lines that decomposes theinterior and boundary centers to obtain the numerical solution of the timedependent PDEs. Then, the method is applied with an adaptive algorithmto obtain the numerical solution of one dimensional problems. We show thatin the problems in which the solutions contain region with rapid variation, the adaptive RBFs methods are successful so that the PDE solution can beapproximated well with a small number of basis functions. The method isdescribed in detail, and computational experiments are performed for one-dimensional Burgers' equations.

In this article, a numerical approximation to the solution of the Newell-Whitehead equation (NWE) and Cauchy problem of ill-posed non-linear dif-fusion equation have been studied. The presented scheme is obtained byusing the derivative of the cubic B-spline quasi-interpolation (BSQI) to ap-proximate the spatial derivative of the dependent variable and  rst orderforward di erence to approximate the time derivative of the dependent vari-able. Some numerical experiments are provided to illustrate the method. The results of numerical experiments are compared with analytical solutions. The main advantage of the scheme is that the algorithm is very simple andvery easy to implement.

We present here the numerical solution of damped forced oscillator prob-lem using Haar wavelet and compare the numerical results obtained withsome well-known numerical methods such as Runge-Kutta fourth order clas-sical and Taylor Series methods. Numerical results show that the presentHaar wavelet method gives more accurate approximations than above saidnumerical methods.