Iranian Journal of Numerical Analysis and Optimization

13-36

Authors: Reza Ghanbari; Aghileh Heydari; Saeed Nezhadhosein

In this paper, a two-phase algorithm, namely IVNS, is proposed for solving nonlinear optimal control problems. In each phase of the algorithm, we use a variable neighborhood search (VNS), which performs a uniform distribution in the shaking step and the successive quadratic programming, as the local search step. In the first phase, VNS starts with a completely random initial solution of control input values. To increase the accuracy of the solution obtained from the phase 1, some new time nodes are added and the values of the new control inputs are estimated by spline interpolation. Next, in the second phase, VNS restarts by the solution constructed by the phase 1. The proposed algorithm is implemented on more than 20 well-known benchmarks and real world problems, then the results are compared with some recently proposed algorithms. The numerical results show that IVNS can find the best solution on 84% of test problems. Also, to compare the IVNS with a common VNS (when the number of time nodes is same in both phases), a computational study is done. This study shows that IVNS needs less computational time with respect to common VNS, when the quality of solutions are not different signifcantly.

49-61

Authors: Ali R. Soheili; Maryam Arab Ameri; M. Barfeie

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

73-83

Authors: Inderdeep Singh; Sheo Kumar

We present here the numerical solution of damped forced oscillator problem using Haar wavelet and compare the numerical results obtained with some well-known numerical methods such as Runge-Kutta fourth order classical and Taylor Series methods. Numerical results show that the present Haar wavelet method gives more accurate approximations than above said numerical methods.