scholarly journals The Chebyshev Wavelet Method for Numerical Solutions of A Fractional Oscillator

2012 ◽  
Vol 1 (4) ◽  
Author(s):  
E. Hesameddini ◽  
S. Shekarpaz ◽  
Habibolla Latifizadeh
Keyword(s):  
Numerical Solutions ◽  
Wavelet Method ◽  
Fractional Oscillator ◽  
Chebyshev Wavelet

Third-Kind Chebyshev Wavelet Method for the Solution of Fractional Order Riccati Differential Equations

2019 ◽  
Vol 28 (14) ◽  
pp. 1950247 ◽  
Author(s):  
Sadiye Nergis Tural-Polat
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Algebraic Equations ◽  
Wavelet Method ◽  
Riccati Differential Equations ◽  
The Third ◽  
Chebyshev Wavelet ◽  
Fractional Orders

In this paper, we derive the numerical solutions of the various fractional-order Riccati type differential equations using the third-kind Chebyshev wavelet operational matrix of fractional order integration (C3WOMFI) method. The operational matrix of fractional order integration method converts the fractional differential equations to a system of algebraic equations. The third-kind Chebyshev wavelet method provides sparse coefficient matrices, therefore the computational load involved for this method is not as severe and also the resulting method is faster. The numerical solutions agree with the exact solutions for non-fractional orders, and also the solutions for the fractional orders approach those of the integer orders as the fractional order coefficient [Formula: see text] approaches to 1.

Chebyshev wavelet method for numerical solutions of integro-differential form of Lane–Emden type differential equations

2017 ◽  
Vol 15 (02) ◽  
pp. 1750015 ◽  
Author(s):  
P. K. Sahu ◽  
S. Saha Ray
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Differential Form ◽  
Present Method ◽  
Numerical Solutions ◽  
Algebraic Equations ◽  
Singular Differential Equation ◽  
Wavelet Method ◽  
Chebyshev Wavelets ◽  
Chebyshev Wavelet

In this paper, Chebyshev wavelet method (CWM) has been applied to solve the second-order singular differential equations of Lane–Emden type. Firstly, the singular differential equation has been converted to Volterra integro-differential equation and then solved by the CWM. The properties of Chebyshev wavelets were first presented. The properties of Chebyshev wavelets via Gauss–Legendre rule were used to reduce the integral equations to a system of algebraic equations which can be solved numerically by Newton’s method. Convergence analysis of CWM has been discussed. Illustrative examples have been provided to demonstrate the validity and applicability of the present method.

A Nonlinear Fractional Oscillator and Its Experimental Identification in Terms of Wavelet Method

2011 ◽  
Author(s):  
Liviu Bereteu ◽  
Gheorghe Eugen Drăgănescu ◽  
Dan Viorel Stănescu ◽  
Madalin Bunoiu ◽  
Iosif Malaescu
Keyword(s):  
Wavelet Method ◽  
Experimental Identification ◽  
Fractional Oscillator
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