Numerical solutions of nonlinear two-dimensional partial Volterra integro-differential equations by Haar wavelet

Babaaghaie, Abdulkarim; Maleknejad, K.

doi:10.1016/j.cam.2016.12.012

Cited by 35 publications

(5 citation statements)

References 17 publications

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“…Therefore a famous Haar collocation method is applied to simulate the results via the use of Matlab-16. The concerned techniques due to Haar has been used in large number of articles (see [42] , [43] , [44] , [45] ). Also it is natural that weather the model we investigate exists in real world for this purpose, numerous fixed point theories were developed in past.…”

Section: Introductionmentioning

confidence: 99%

Haar wavelet collocation approach for the solution of fractional order COVID-19 model using Caputo derivative

Shah

Khan

Ali³

et al. 2020

Alexandria Engineering Journal

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This article is devoted to study a compartmental mathematical model for the transmission dynamics of the novel Coronavirus-19 under Caputo fractional order derivative. By using fixed point theory of Schauder’s and Banach we establish some necessary conditions for existence of at least one solution to model under investigation and its uniqueness. After the existence a general numerical algorithm based on Haar collocation method is established to compute the approximate solution of the model. Using some real data we simulate the results for various fractional order using Matlab to reveal the transmission dynamics of the current disease due to Coronavirus-19 through graphs.

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Section: Introductionmentioning

confidence: 99%

Haar wavelet collocation approach for the solution of fractional order COVID-19 model using Caputo derivative

Shah

Khan

Ali³

et al. 2020

Alexandria Engineering Journal

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“…For example, Aziz et al [4] developed a collocation method based on Haar wavelet to achieve the numerical solutions of diffusion and reaction-diffusion PVIDEs. Haar wavelets were also applied by Babaghaie and Maleknejad [6] and Kumar and Vijesh [23] to solve nonlinear PVIDEs. In Khan et al [22], Mohsin and Mohammed used two computational semi-analytic methods for solving a class of two-dimensional PVIDEs of fractional order.…”

Section: Introductionmentioning

confidence: 99%

“…Partial integro‐differential equations arise in problems of applied sciences and engineering to model dynamical systems; they can be found in financial mathematics [1–29], biological models [17], fluid dynamics [5], and many other areas. Partial Volterra integro‐differential equations (PVIDEs) have many different types, such as elliptic [30], hyperbolic [12], and parabolic [21] in one‐ or multidimensional, that is why numerous numerical schemes have been well‐evaluated by researchers to approximate the solution of these equations.…”

Section: Introductionmentioning

confidence: 99%

Taylor collocation method for solving two‐dimensional partial Volterra integro‐differential equations

Khennaoui

Bellour

Laib

2023

Math Methods in App Sciences

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In this paper, the numerical solution of a two-dimensional partial Volterra integro-differential equation (2D-PVIDE) is provided by extending the Taylor collocation scheme of one-dimensional Volterra integral equations. The method is based on the use of Taylor polynomials in two-dimensional, while the approximate solution is given by using explicit schemes. The method is proved to be high-order convergent with respect to the maximum norm. Some numerical examples are given to verify the theoretical results.

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“…Operational matrix technique has received considerable attention from numerous researchers for solving dynamical system analysis 6 , system identification 7 , numerical computation of integral and differential equations 8 , and solving systems of PDEs 9 . In addition, Hsiao and Wang 10 introduced the application of Haar wavelets to solve optimal control for linear time-varying systems.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution for Linear State Space Systems using Haar Wavelets Method

Ali

Ali²

2022

Baghdad Sci.J

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In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation vec to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to  . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

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Numerical solutions of nonlinear two-dimensional partial Volterra integro-differential equations by Haar wavelet

Cited by 35 publications

References 17 publications

Haar wavelet collocation approach for the solution of fractional order COVID-19 model using Caputo derivative

Haar wavelet collocation approach for the solution of fractional order COVID-19 model using Caputo derivative

Taylor collocation method for solving two‐dimensional partial Volterra integro‐differential equations

Numerical Solution for Linear State Space Systems using Haar Wavelets Method

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