Numerical method for the solution of special nonlinear fourth-order boundary value problems

El-Gamel, Mohamed; Behiry, S. H.; Hashish, Hagar A

doi:10.1016/s0096-3003(03)00269-8

Cited by 43 publications

(35 citation statements)

References 18 publications

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“…The maximum absolute error obtained by the present method is 4.075 8 10 − × using 5 iterations. The maximum absolute error has been obtained so far by ElGamel et al 18 …”

Section: Numerical Resultsmentioning

confidence: 81%

Numerical Solutions of General Fourth Order Two Point Boundary Value Problems by Galerkin Method with Legendre Polynomials

Hossain

Islam

2015

Dhaka Univ. J. Sci.

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In this paper, Galerkin weighted residual method is presented to find the numerical solutions of the general fourth order linear and nonlinear differential equations with essential boundary conditions. For this, the given differential equations and the boundary conditions over arbitrary finite domain [a, b] are converted into its equivalent form over the interval [0,1]. Here the Legendre polynomials, over the interval [0,1], are chosen as trial functions satisfying the corresponding homogeneous form of the Dirichlet boundary conditions. Details matrix formulations are derived for solving linear and nonlinear boundary value problems (BVPs). Numerical examples for both linear and nonlinear BVPs are considered to verify the proposed formulation and the results obtained are compared.

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“…The maximum absolute error obtained by the present method is 4.075 8 10 − × using 5 iterations. The maximum absolute error has been obtained so far by ElGamel et al 18 …”

Section: Numerical Resultsmentioning

confidence: 81%

Numerical Solutions of General Fourth Order Two Point Boundary Value Problems by Galerkin Method with Legendre Polynomials

Hossain

Islam

2015

Dhaka Univ. J. Sci.

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“…We also require derivatives of composite Sinc functions evaluated at the nodes. The expressions required for the present discussion are [11].…”

Section: And On the Boundary Of D E (Denoted ∂D E ) Satisfymentioning

confidence: 99%

Numerical Study of Second Painlevé Equation

Saadatmandi¹

2012

Communications in Numerical Analysis

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“…Some numerical and analytical methods such as shooting method [5], Finite-element method [6], sincGalerkin method [7], finite-difference method [8], Adomian technique [9], variational iteration method (VIM) [10], homotopy perturbation method (HPM) [11], analysis method (HAM) [12], have been studied for obtaining approximate solutions to boundary value problems.…”

Section: Introductionmentioning

confidence: 99%

A New Analytical Approach for Solving Nonlinear Boundary Value Problems in Finite Domains

Biazar¹,

Ghanbari²

2011

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Based on the homotopy analysis method (HAM), we propose an analytical approach for solving the following type of nonlinear boundary value problems in finite domain. In framework of HAM a convenient way to adjust and control the convergence region and rate of convergence of the obtained series solutions, by defining the so-called control parameter , is provided. This paper aims to propose an efficient way of finding the proper values of . Such values of parameter can be determined at the any order of approximations of HAM series solutions by solving of a nonlinear polynomial equation. Some examples of nonlinear initial value problems in finite domain are used to illustrate the validity of the proposed approach. Numerical results confirm that obtained series solutions agree very well with the exact solutions.

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Numerical method for the solution of special nonlinear fourth-order boundary value problems

Cited by 43 publications

References 18 publications

Numerical Solutions of General Fourth Order Two Point Boundary Value Problems by Galerkin Method with Legendre Polynomials

Numerical Solutions of General Fourth Order Two Point Boundary Value Problems by Galerkin Method with Legendre Polynomials

Numerical Study of Second Painlevé Equation

A New Analytical Approach for Solving Nonlinear Boundary Value Problems in Finite Domains

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