A numerical method for fractional variable order pantograph differential equations based on Haar wavelet

2021 ◽  
Author(s):  
Hussam Alrabaiah ◽  
Israr Ahmad ◽  
Rohul Amin ◽  
Kamal Shah
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Haar Wavelet ◽  
Variable Order

Variable-step-size second-order-derivative multistep method for solving first-order ordinary differential equations in system simulation

2020 ◽  
Vol 11 (01) ◽  
pp. 2050001
Author(s):  
Lei Zhang ◽  
Chaofeng Zhang ◽  
Mengya Liu
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Multistep Method ◽  
Second Order ◽  
Order Derivative ◽  
Variable Step Size ◽  
Variable Order ◽  
Step Size ◽  
Variable Step ◽  
The Stability

According to the relationship between truncation error and step size of two implicit second-order-derivative multistep formulas based on Hermite interpolation polynomial, a variable-order and variable-step-size numerical method for solving differential equations is designed. The stability properties of the formulas are discussed and the stability regions are analyzed. The deduced methods are applied to a simulation problem. The results show that the numerical method can satisfy calculation accuracy, reduce the number of calculation steps and accelerate calculation speed.

Numerical Solution of Diffusion and Reaction–Diffusion Partial Integro-Differential Equations

2018 ◽  
Vol 15 (06) ◽  
pp. 1850047 ◽  
Author(s):  
Imran Aziz ◽  
Imran Khan
Keyword(s):  
Population Dynamics ◽  
Differential Equations ◽  
Numerical Solution ◽  
Numerical Method ◽  
Reaction Diffusion ◽  
Nonlinear Problems ◽  
Haar Wavelet ◽  
Benchmark Problems ◽  
Two Dimensional ◽  
One Dimensional

In this paper, a collocation method based on Haar wavelet is developed for numerical solution of diffusion and reaction–diffusion partial integro-differential equations. The equations are parabolic partial integro-differential equations and we consider both one-dimensional and two-dimensional cases. Such equations have applications in several practical problems including population dynamics. An important advantage of the proposed method is that it can be applied to both linear as well as nonlinear problems with slide modification. The proposed numerical method is validated by applying it to various benchmark problems from the existing literature. The numerical results confirm the accuracy, efficiency and robustness of the proposed method.

scholarly journals Haar wavelet method for solution of variable order linear fractional integro-differential equations

2022 ◽  
Vol 7 (4) ◽  
pp. 5431-5443
Author(s):  
Rohul Amin ◽  
◽  
Kamal Shah ◽  
Hijaz Ahmad ◽  
Abdul Hamid Ganie ◽  
...  
Keyword(s):  
Differential Equations ◽  
Haar Wavelet ◽  
Variable Order ◽  
Algebraic Equations ◽  
Elimination Algorithm ◽  
Collocation Technique ◽  
Gauss Elimination ◽  
Collocation Scheme ◽  
The Given ◽  
Derivatives Of

<abstract><p>In this paper, we developed a computational Haar collocation scheme for the solution of fractional linear integro-differential equations of variable order. Fractional derivatives of variable order is described in the Caputo sense. The given problem is transformed into a system of algebraic equations using the proposed Haar technique. The results are obtained by solving this system with the Gauss elimination algorithm. Some examples are given to demonstrate the convergence of Haar collocation technique. For different collocation points, maximum absolute and mean square root errors are computed. The results demonstrate that the Haar approach is efficient for solving these equations.</p></abstract>

Steady-state modelling method for matrix-reactance frequency converter with boost topology

2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Double Fourier Series ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Modelling Method ◽  
Three Phase

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

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