The Legendre wavelet method for solving initial value problems of Bratu-type

Venkatesh, S.; Ayyaswamy, S. K.; Balachandar, S.

doi:10.1016/j.camwa.2011.12.069

Cited by 69 publications

(36 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several numerical techniques had been applied to obtain the approximate solution of the Bratu-type problem. For example spline method [2][3], wavelet method [4][5][6], spectral method [7][8][9][10] and Adomain decomposition method [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Solution of Initial Value Prpblem of Bratu – Type Equation using Modifications of Homotopy Perturbation Method

Kashkari¹,

Abbas²

2017

IJCA

View full text Add to dashboard Cite

Homotopy perturbation method (HPM) is an effective method for solving nonlinear differential equations. In this paper, some modifications of this method has been proposed to initial value problem of Bratu -Type model. The combination of Laplace transform and homotopy perturbation (LHPM), the new homotopy perturbation method (NHPM) and Laplace new homotopy perturbation method (LNHPM) are applied, and the solutions are considered as an infinite series that converge rapidly to the exact solutions. KeywordsBratu -Type equation, Homotopy perturbation method, Laplace homotopy perturbation method, new homotopy perturbation method, Laplace new homotopy perturbation method

show abstract

Section: Introductionmentioning

confidence: 99%

Solution of Initial Value Prpblem of Bratu – Type Equation using Modifications of Homotopy Perturbation Method

Kashkari¹,

Abbas²

2017

IJCA

View full text Add to dashboard Cite

show abstract

“…Many methods havebeen developed for solving these equations numerically since most of them either have no analytical solution or are quite di cult to solve. Some numerical methods in the literature include the following: the variational iteration method [1][2][3], the homotopy analysis method [4][5][6][7], the Adomian decomposition method [8][9][10], the homotopy perturbation method [11,12], the Haar wavelet method [13,14], the Chebyshev wavelets method [15] and the Legendre wavelets method [16,17].…”

Section: Introductionmentioning

confidence: 99%

Solving nonlinear boundary value problems by the Galerkin method with sinc functions

Alkan

Seçer

2015

Open Physics

View full text Add to dashboard Cite

Abstract:In this paper, the sinc-Galerkin method is used for numerically solving a class of nonlinear di erential equations with boundary conditions. The importance of this study is that sinc approximation of the nonlinear term is stated as a new theorem. The method introduced here is tested on some nonlinear problems and is shown to be a very e cient and powerful tool for obtaining approximate solutions of nonlinear ordinary di erential equations.

show abstract

“…There are several other wavelets which can be used to solve the differential equations. Some of these include, Daubechies [8,32], B-spline [9], Legendre [29,35], Hermite [1,33] and Chebyshev [3,17]. Legendre, Hermite and Chebyshev wavelets uses Legendre, Hermite and Chebyshev polynomials as their basis functions, respectively.…”

Section: Introductionmentioning

confidence: 99%

Gegenbauer Wavelets Operational Matrix Method for Fractional Differential Equations

Rehman¹,

Saeed²

2015

Journal of the Korean Mathematical Society

View full text Add to dashboard Cite

Abstract. In this article we introduce a numerical method, named Gegenbauer wavelets method, which is derived from conventional Gegenbauer polynomials, for solving fractional initial and boundary value problems. The operational matrices are derived and utilized to reduce the linear fractional differential equation to a system of algebraic equations. We perform the convergence analysis for the Gegenbauer wavelets method.We also combine Gegenbauer wavelets operational matrix method with quasilinearization technique for solving fractional nonlinear differential equation. Quasilinearization technique is used to discretize the nonlinear fractional ordinary differential equation and then the Gegenbauer wavelet method is applied to discretized fractional ordinary differential equations. In each iteration of quasilinearization technique, solution is updated by the Gegenbauer wavelet method. Numerical examples are provided to illustrate the efficiency and accuracy of the methods.

show abstract

The Legendre wavelet method for solving initial value problems of Bratu-type

Cited by 69 publications

References 19 publications

Solution of Initial Value Prpblem of Bratu – Type Equation using Modifications of Homotopy Perturbation Method

Solution of Initial Value Prpblem of Bratu – Type Equation using Modifications of Homotopy Perturbation Method

Solving nonlinear boundary value problems by the Galerkin method with sinc functions

Gegenbauer Wavelets Operational Matrix Method for Fractional Differential Equations

Contact Info

Product

Resources

About