scholarly journals Generalized Haar wavelet operational matrix method for solving hyperbolic heat conduction in thin surface layers

2018 ◽  
Vol 11 ◽  
pp. 243-252 ◽  
Author(s):  
Suazlan Mt Aznam ◽  
M.S.H. Chowdhury
Keyword(s):  
Heat Conduction ◽  
Matrix Method ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
Hyperbolic Heat Conduction ◽  
Surface Layers ◽  
Operational Matrix Method

Haar Wavelet Operational Matrix Method for the Numerical Solution of Fractional Order Differential Equations

2015 ◽  
Vol 4 (4) ◽  
Author(s):  
Firdous A. Shah ◽  
R. Abbas
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Matrix Method ◽  
Present Method ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
Haar Wavelets ◽  
Operational Matrix Method ◽  
Fractional Order Differential Equations ◽  
Block Pulse Functions

AbstractIn this paper, we propose a new operational matrix method of fractional order integration based on Haar wavelets to solve fractional order differential equations numerically. The properties of Haar wavelets are first presented. The properties of Haar wavelets are used to reduce the system of fractional order differential equations to a systemof algebraic equationswhich can be solved numerically byNewton’s method.Moreover, the proposed method is derived without using the block pulse functions considered in open literature and does not require the inverse of the Haar matrices. Numerical examples are included to demonstrate the validity and applicability of the present method.

scholarly journals Haar Wavelet Operational Matrix Method for Fractional Oscillation Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Umer Saeed ◽  
Mujeeb ur Rehman
Keyword(s):  
Exact Solution ◽  
Fractional Order ◽  
Nonlinear Oscillation ◽  
Matrix Method ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
The Other ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Operational Matrix Method

We utilized the Haar wavelet operational matrix method for fractional order nonlinear oscillation equations and find the solutions of fractional order force-free and forced Duffing-Van der Pol oscillator and higher order fractional Duffing equation on large intervals. The results are compared with the results obtained by the other technique and with exact solution.

scholarly journals Φ -Haar Wavelet Operational Matrix Method for Fractional Relaxation-Oscillation Equations Containing Φ -Caputo Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Pongsakorn Sunthrayuth ◽  
Noufe H. Aljahdaly ◽  
Amjid Ali ◽  
Rasool Shah ◽  
Ibrahim Mahariq ◽  
...  
Keyword(s):  
Numerical Method ◽  
Matrix Method ◽  
Relaxation Oscillation ◽  
Operational Matrix ◽  
Relaxation Oscillator ◽  
Haar Wavelet ◽  
Algebraic Equations ◽  
Operational Matrix Method ◽  
Linear Algebraic Equations ◽  
Fractional Relaxation

This paper proposes a numerical method for solving fractional relaxation-oscillation equations. A relaxation oscillator is a type of oscillator that is based on how a physical system returns to equilibrium after being disrupted. The primary equation of relaxation and oscillation processes is the relaxation-oscillation equation. The fractional derivatives in the relaxation-oscillation equations under consideration are defined in the Φ -Caputo sense. The numerical method relies on a novel type of operational matrix method, namely, the Φ -Haar wavelet operational matrix method. The operational matrix approach has a lower computational complexity. The proposed scheme simplifies the main problem to a set of linear algebraic equations. Numerical examples demonstrate the validity and applicability of the proposed technique.

Haar wavelet operational matrix method for system of fractional nonlinear differential equations

2017 ◽  
Vol 15 (05) ◽  
pp. 1750043 ◽  
Author(s):  
Umer Saeed
Keyword(s):  
Differential Equations ◽  
Reliable Method ◽  
Nonlinear Differential Equations ◽  
Operational Matrix ◽  
Implementation Process ◽  
Haar Wavelet ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Operational Matrix Method ◽  
Fractional Differential

In this paper, we present a reliable method for solving system of fractional nonlinear differential equations. The proposed technique utilizes the Haar wavelets in conjunction with a quasilinearization technique. The operational matrices are derived and used to reduce each equation in a system of fractional differential equations to a system of algebraic equations. Convergence analysis and implementation process for the proposed technique are presented. Numerical examples are provided to illustrate the applicability and accuracy of the technique.

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