A New Spectral-Collocation Method Using Legendre Multi-wavelets for Solving of Nonlinear Fractional Differential Equations
Journal Title: Journal of Advances in Mathematics and Computer Science - Year 2017, Vol 21, Issue 4
Abstract
In this paper, a novel spectral collocation method using Legendre multi-wavelets as the basis functions is presented to obtain the numerical solution of nonlinear fractional differential equations. The fractional derivative is described in the Caputo sense. The two-scale relations of Legendre multi-wavelets and the properties of block pulse functions have been used in the evaluation of the fractional integral operational matrix and expansion coefficients of the nonlinear terms for the Legendre multi-wavelets. Due to the aforementioned properties, the original differential equation is converted into a nonlinear system of algebraic equations which can be solved by existing tools. The numerical results are compared with exact solutions and existing numerical solutions found in the literature and demonstrate the validity and applicability of the proposed method.
Authors and Affiliations
Fukang Yin
Keywords
Related Articles
- EP ID EP322123
- DOI 10.9734/BJMCS/2017/32628
- Views 99
- Downloads 0
The Mathematical Proof for the Beal Conjecture
The Beal conjecture is a number theory formulated in 1993 by the billionaire banker, Mr Andrew Beal. Mr Beal, very recently, declared a one-million-dollar award for the proof of this number theory. As at present, no proo...
Estimation in Step-stress Partially Accelerated Life Test for Exponentiated Pareto Distribution under Progressive Censoring with Random Removal
Accelerated life testing or partially accelerated life testing is generally used in manufacturing industries since it affords significant minimization in the cost and test time. In this paper, a step-stress partially acc...
Convergence Analysis of a Non-overlapping DDM for Optimal Absorbing Boundary Control Problems Governed by Wave Equations
A non-overlapping domain decomposition method (DDM) is described to solve optimal boundary control problems governed by wave equations with absorbing boundary condition. The whole domain is divided into non-overlapping s...
Existence and Uniqueness of Positive Periodic Solution of an Extended Rosenzweig-MacArthur Model via Brouwer's Topological Degree
The necessary conditions for existence of periodic solutions of an Extended Rosenzweig- MacArthur model are obtained using Brouwer’s degree. The forward invariant set is formulated to ensure the boundedness of the soluti...
Mathematical Model of Drinking Epidemic
A non-linear SHTR mathematical model was used to study the dynamics of drinking epidemic. We discussed the existence and stability of the drinking-free and endemic equilibria. The drinking-free equilibrium was locally as...