A wavelet Petrov–Galerkin method for solving integro-differential equations

Summary In this paper, a numerical method for solving time‐varying delay equations and optimal control problems with time‐varying delay systems is discussed. This method is based upon Fibonacci wavelets and Petrov‐Galerkin method. To solve these problems, first, the Fibonacci wavelets are presented. With the aid of operational matrices of integration and delay for Fibonacci wavelets and using Petrov‐Galerkin method and Newton's iterative method, we solve two classes of time‐varying delay problems, numerically. The approximate solutions achieved by this method satisfy all the initial conditions. In addition, an estimation of the error is given. Numerical results are included to demonstrate the accuracy and applicability of the present technique.

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“…The resulting equation can be solved using Petrov‐Galerkin method that is convergence . For this approach, we have

Y = ⟨ \tilde{Φ}, φ ⟩,

where Y =0 and φ ( t ) is an arbitrary function.…”

Section: Methodsmentioning

confidence: 99%

“…The resulting equation can be solved using Petrov-Galerkin method that is convergence. 44 For this approach, we have…”

Section: Problemmentioning

confidence: 99%

Fibonacci wavelets and their applications for solving two classes of time‐varying delay problems

Sabermahani

Ordokhani

Yousefi

2019

Optim Control Appl Methods

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“…At first we introduce some of methods for solving integral equations and integro-differential equations. In [1,6] authors used from numerical methods for solving Fredholm integral equations also in [8] Fredholm integro-differential was solved by wavelet Petrov-Galerkin method. One application of the above equation is in chemical absorption kinetics, see [5].…”

Section: Introductionmentioning

confidence: 99%

Solving Of Nonlinear System Of Fredholm-volterra Integro-differential Equations By Using Discrete Collocation Method

Rabbani¹,

Kiasoltani²

2011

J. Math. Computer Sci.

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In this paper, we solve nonlinear system of Fredholm-Volterra integro-differential equations by using discrete collocation method. These types of systems of integral equations are important and they can be used in engineering and some of the applied sciences such as population dynamics, reaction-diffusion in small cells and models of epidemic diffusion. Also these equations with convolution kernel can be solved by discrete collocation method. By the above mentioned method we approximate solution of equation by no smooth piecewise polynomials, for validity and ability the method we solve some examples with high accuracy.

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“…The numerical method employed in [1] was the Galerkin method. In [4,5], the wavelet Petrov-Galerkin schemes based on discontinuous orthogonal multiwavelets were described. InthispaperweuseAlpert'smultiwaveletsbyusing Petrov-Galerkin method.…”

mentioning

confidence: 99%

Numerical Solution Of Singular Fredholm Integrodifferential Equations Of The Second Kind Via Petrovgalerkin Method By Using Legendre Multiwavelet

Akhavan

2014

J. Math. Computer Sci.

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It is of interest to know whether we can solve a singular Fredholm integro-differential equation of the second kind with an infinite or semi-infinite range of integrate via Petrov-Galerkin method by using Legendre multiwavelet. For this purpose, we directly deal with infinite range of integrate. We introduce some change of variables for mapping infinite interval into a finite interval. After that, we use Petrov-Galerkin method with Legendre multiwavelet basis that yields linear system. Numerical results of our example will demonstrate accuracy and efficiency of the proposed method.

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A wavelet Petrov–Galerkin method for solving integro-differential equations

Cited by 7 publications

References 5 publications

Fibonacci wavelets and their applications for solving two classes of time‐varying delay problems

Fibonacci wavelets and their applications for solving two classes of time‐varying delay problems

Solving Of Nonlinear System Of Fredholm-volterra Integro-differential Equations By Using Discrete Collocation Method

Numerical Solution Of Singular Fredholm Integrodifferential Equations Of The Second Kind Via Petrovgalerkin Method By Using Legendre Multiwavelet

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