Orthogonal cubic spline collocation method for the extended Fisher–Kolmogorov equation

Danumjaya, P.; Pani, Amiya K.

doi:10.1016/j.cam.2004.04.002

Cited by 76 publications

(37 citation statements)

References 19 publications

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“…The actual errors are also computed to compare with the error bounds obtained in Section IV. The present work naturally complements and extends several known results for the continuous case [1], [2], [5], [6], [7], [11], [12], [14], [15], [16], [17], [18], as well as the research done on cubic discrete spline interpolation [19].…”

Section: Introductionsupporting

confidence: 79%

Approximation by discrete spline interpolation

Chen

Wong

2010

2010 11th International Conference on Control Automation Robotics &Amp; Vision

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For a function ( ) defined on the discrete interval [ , + 2] = { , + 1, ⋅ ⋅ ⋅ , + 2}, we develop a class of quintic discrete spline interpolate ( ) that involves only differences. Further, explicit error bounds are offered in the form of the inequalitywhere the constants , 2 ≤ ≤ 6 are explicitly provided. Three numerical examples are presented to illustrate the actual construction of the discrete spline interpolates, the actual errors are also computed to compare with the error bounds obtained.Index Terms-discrete spline interpolation, quintic polynomials, error estimates.

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Section: Introductionsupporting

confidence: 79%

Approximation by discrete spline interpolation

Chen

Wong

2010

2010 11th International Conference on Control Automation Robotics &Amp; Vision

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“…Following Qiang and Nicolaides [27], X. Ye [29], X. Ye and X. Cheng [30], P. Danumjaya and Amiya K. Pani [28], we define…”

Section: Commentsmentioning

confidence: 98%

Finite difference approximate solutions for the Cahn‐Hilliard equation

Khiari

Achouri

Mohamed

et al. 2006

Numerical Methods Partial

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In this article, we analyze a Crank-Nicolson-type finite difference scheme for the nonlinear evolutionary Cahn-Hilliard equation. We prove existence, uniqueness and convergence of the difference solution. An iterative algorithm for the difference scheme is given and its convergence is proved. A linearized difference scheme is presented, which is also second-order convergent. Finally a new difference method possess a Lyapunov function is presented.

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“…In computational studies, especially in [8] Danumjaya and Pani have proposed a finite element Galerkin method for the EFK equation and in [9] they analyzed a second-order splitting combined with an orthogonal cubic spline collocation method, there is hardly any numerical approximation to (1.1)-(1.3) with finite differences which we consider in this article.…”

Section: Introductionmentioning

confidence: 98%

A second-order accurate difference scheme for an extended Fisher–Kolmogorov equation

Kadri

Omrani

2011

Computers & Mathematics with Applications

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a b s t r a c tIn this paper, we present a Crank-Nicolson type finite difference scheme to approximate the nonlinear evolutionary Extended Fisher-Kolmogorov (EFK) equation. We prove the existence of the solution by using the well-known Browder fixed-point theorem. The stability of this scheme is established in L ∞ -norm. The uniqueness and convergence of the solution are analyzed. We discuss an iterative algorithm for solving the difference scheme and prove its convergence.

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Orthogonal cubic spline collocation method for the extended Fisher–Kolmogorov equation

Cited by 76 publications

References 19 publications

Approximation by discrete spline interpolation

Approximation by discrete spline interpolation

Finite difference approximate solutions for the Cahn‐Hilliard equation

A second-order accurate difference scheme for an extended Fisher–Kolmogorov equation

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