Quasilinearized Scale-3 Haar wavelets-based algorithm for numerical simulation of fractional dynamical systems. Issue 5 (24th August 2018)

• Record Type: Journal Article
• Authors: Mittal, R.C.; Pandit, Sapna
• Is Part Of: Engineering computations. Volume 35:Issue 5(2018)
• Page Start: 1907
• Page End: 1931
• Publication Date: 2018-08-24
• Subjects: Fractional differential equation -- Quasilinearization technique -- Scale-3 Haar wavelets; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-09-2017-0347
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The main purpose of this work is to develop a novel algorithm based on Scale-3 Haar wavelets (S-3 HW) and quasilinearization for numerical simulation of dynamical system of ordinary differential equations. Design/methodology/approach: The first step in the development of the algorithm is quasilinearization process to linearize the problem, and then Scale-3 Haar wavelets are used for space discretization. Finally, the obtained system is solved by Gauss elimination method. Findings: Some numerical examples of fractional dynamical system are considered to check the accuracy of the algorithm. Numerical results show that quasilinearization with Scale-3 Haar wavelet converges fast even for small number of collocation points as compared of classical Scale-2 Haar wavelet (S-2 HW) method. The convergence analysis of the proposed algorithm has been shown that as we increase the resolution level of Scale-3 Haar wavelet error goes to zero rapidly. Originality/value: To the best of authors' knowledge, this is the first time that new Haar wavelets Scale-3 have been used in fractional system. A new scheme is developed for dynamical system based on new Scale-3 Haar wavelets. These wavelets take less time than Scale-2 Haar wavelets. This approach extends the idea of Jiwari (2015, 2012 ) via translation and dilation of Haar function at Scale-3.