Quasilinearized Scale-3 Haar wavelets-based algorithm for numerical simulation of fractional dynamical systems

• Published in: Engineering computations Vol. 35; no. 5; pp. 1907 - 1931
• Main Authors: Mittal, R.C., Pandit, Sapna
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Publishing Limited 05-09-2018; Emerald Group Publishing Limited
• Subjects: Algorithms; Calculus; Computer simulation; Convergence; Differential equations; Dynamical systems; Gaussian elimination; Mathematical models; Methods; Numerical analysis; Wavelet analysis; Fractional differential equation; Quasilinearization technique; Scale-3 Haar wavelets
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/EC-09-2017-0347

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.