Shifted Chebyshev direct method for solving variational problems

Horng, Ing-Rong; Chou, Jyh–Horng

doi:10.1080/00207728508926718

Cited by 94 publications

(32 citation statements)

References 8 publications

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“…The approach is based on converting the underlying differential equations into an integral equation through integration, approximating various signals involved in the equation by truncated orthogonal series, and using the operational matrix of integration P to eliminate the integral operations. Typical examples are the Walsh functions [1], block-pulse functions [2], Legendre polynomials [3], Chebyshev polynomials [4], Fourier series [5], Haar series [6] and Hartley series [7]. The utilization of these series have the common objective of representing models efficiently and calculating intermediate parameters rapidly for the given problem.…”

Section: Introductionmentioning

confidence: 98%

Solution of Volterra's population model via block‐pulse functions and Lagrange‐interpolating polynomials

Marzban

Hoseini

Razzaghi

2008

Math Methods in App Sciences

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SUMMARYA numerical method for solving Volterra's population model for population growth of a species in a closed system is proposed. Volterra's model is a nonlinear integro-differential equation where the integral term represents the effects of toxin. The approach is based on hybrid function approximations. The properties of hybrid functions that consist of block-pulse and Lagrange-interpolating polynomials are presented. The associated operational matrices of integration and product are then utilized to reduce the solution of Volterra's model to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. Applications are demonstrated through an illustrative example.

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Section: Introductionmentioning

confidence: 98%

Solution of Volterra's population model via block‐pulse functions and Lagrange‐interpolating polynomials

Marzban

Hoseini

Razzaghi

2008

Math Methods in App Sciences

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“…In spectral methods [11,20,21] a function X(x), square integrable in [0, 1) , may be approximated by using orthogonal functions (OFs) as…”

Section: The Finite Difference and Spectral Methodsmentioning

confidence: 99%

Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition

Ramezani

Dehghan

Razzaghi

2007

Numerical Methods Partial

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In this work the combined finite difference and spectral methods have been proposed for the numerical solution of the one-dimensional wave equation with an integral condition. The time variable is approximated using a finite difference scheme. But the spectral method is employed for discretizing the space variable. The main idea behind this approach is that we can get high-order results. The new method is used for two test problems and the numerical results are obtained to support our theoretical expectations.

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“…Then unknown coefficients are expanded with composite spectral (denoted CS in this article) function with unknown constant coefficients. These CS functions, which consist of few terms of orthogonal functions are given [24,27,28].…”

Section: Introductionmentioning

confidence: 99%

Composite spectral method for solution of the diffusion equation with specification of energy

Dehghan

Ramezani

2007

Numerical Methods Partial

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Many physical subjects are modeled by nonclassical parabolic boundary value problems with nonlocal boundary conditions replacing the classic boundary conditions. In this article, we introduce a new numerical method for solving the one-dimensional parabolic equation with nonlocal boundary conditions. The approximate proposed method is based upon the composite spectral functions. The properties of composite spectral functions consisting of terms of orthogonal functions are presented and are utilized to reduce the problem to some algebraic equations. The method is easy to implement and yields very accurate result.

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Shifted Chebyshev direct method for solving variational problems

Cited by 94 publications

References 8 publications

Solution of Volterra's population model via block‐pulse functions and Lagrange‐interpolating polynomials

Solution of Volterra's population model via block‐pulse functions and Lagrange‐interpolating polynomials

Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition

Composite spectral method for solution of the diffusion equation with specification of energy

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