The Petrov-Galerkin Method and Chebyshev Multiwavelet Basis for Solving Integro-Differential Equations

Authors

  • M. Rabbani
Abstract:

 Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For numerical examples, the solutions may be produced with good accuracy, by choosing suitable trial and test spaces in Petrov-Galerkin method.  

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Existence of solution and solving the integro-differential equations system by the multi-wavelet Petrov-Galerkin method

‎In this paper, we discuss about existence of solution for integro-differential system and then we solve it  by using the Petrov-Galerkin method. In the Petrov-Galerkin method choosing the trial and test space is important, so we use Alpert multi-wavelet as basis functions for these spaces. Orthonormality is one of the properties of Alpert multi-wavelet which helps us to reduce computations in ...

full text

Fractional type of flatlet oblique multiwavelet for solving fractional differential and integro-differential equations

The construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. We apply this system as basis functions to solve the fractional differential and integro-differential equations. Biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. Some test pr...

full text

The Legendre Wavelet Method for Solving Singular Integro-differential Equations

In this paper, we present Legendre wavelet method to obtain numerical solution of a singular integro-differential equation. The singularity is assumed to be of the Cauchy type. The numerical results obtained by the present method compare favorably with those obtained by various Galerkin methods earlier in the literature.

full text

Shifted Chebyshev Approach for the Solution of Delay Fredholm and Volterra Integro-Differential Equations via Perturbed Galerkin Method

The main idea proposed in this paper is the perturbed shifted Chebyshev Galerkin method for the solutions of delay Fredholm and Volterra integrodifferential equations. The application of the proposed method is also extended to the solutions of integro-differential difference equations. The method is validated using some selected problems from the literature. In all the problems that are considered...

full text

Flatlet Oblique Multiwavelet for Solving Integro-differential Equations

In this paper we construct a flatlet biorthogonal multiwavelets System. Then, we use this system for numerical solution of Integro-differential equations. The good properties of this system, i.e., biorthogonality and more vanishing moments lead to efficient and accurate solutions. Some test problems with known solutions are presented and the numerical results are given to show the efficiency of...

full text

existence of solution and solving the integro-differential equations system by the multi-wavelet petrov-galerkin method

‎in this paper, we discuss about existence of solution forintegro-differential system and then we solve it  by using the petrov-galerkin method. in the petrov-galerkin method choosing the trial and test space is important, so  we use alpert multi-wavelet as basisfunctions for these spaces. orthonormality is one of theproperties of alpert multi-wavelet which helps us to reducecomputations in the...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 18  issue 1

pages  19- 26

publication date 2007-01

By following a journal you will be notified via email when a new issue of this journal is published.

Keywords

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023