A Multilevel Wavelet Collocation Method for Solving Partial Differential Equations in a Finite Domain

Vasilyev, Oleg V.; Paolucci, Samuel; Sen, Mihir

doi:10.1006/jcph.1995.1147

Cited by 93 publications

(97 citation statements)

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“…Wavelet methods are closely connected to point-grid based methods that also generalize to higher than one dimensions [158,159]. Lippert et al [160] have used interpolating wavelets in point-grid based methods.…”

Section: Solution Of Atomic Orbitals Using Interpolating Waveletsmentioning

confidence: 99%

Three real‐space discretization techniques in electronic structure calculations

Torsti

Eirola²,

Enkovaara

et al. 2006

Physica Status Solidi (b)

106

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Published online zzz PACS 71.15.Ap, 71.15.Dx A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.

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Section: Solution Of Atomic Orbitals Using Interpolating Waveletsmentioning

confidence: 99%

Three real‐space discretization techniques in electronic structure calculations

Torsti

Eirola²,

Enkovaara

et al. 2006

Physica Status Solidi (b)

106

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“…For this reason, they seem particularly adaptable to approximate functions with local lack of regularity like the solutions of some partial differential equations. In recent years, many effective numerical method for PDEs based on wavelets have been proposed [1][2][3], such as the wavelet Galerkin method (WGM), the wavelet finite element method and the wavelet collocation method etc.…”

Section: Introductionmentioning

confidence: 99%

Adaptive interpolation wavelet and homotopy perturbation method for partial differential equations

Ma¹,

Mei²

2008

J. Phys.: Conf. Ser.

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Abstract. The homotopy perturbation method proposed by Ji-Huan He has been developed to solve nonlinear matrix differential equations. This paper constructs an adaptive multilevel quasi-wavelet operator according to the interpolation wavelet theory, with which the nonlinear partial differential equations can be discretized adaptively in physical spaces as a matrix differential equation, its numerical solution can be obtained by using the homotopy perturbation method. Numerical results show that the homotopy perturbation method is not sensitive to the time step, so the arithmetic error mainly arises in the space step. Burgers equation is taken as examples to illustrate its effectiveness and convenience.

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“…The adaptive wavelet collocation method provided a mathematical foundation in the field of science and engineering [8,10,15]. The main objective of this paper is to present AGHWCM, an alternative method to existing ones for the numerical solution of parabolic PDEs.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of parabolic partial differential equations using adaptive gird Haar wavelet collocation method

Shiralashetti

Angadi²,

Kantli

et al. 2016

Asian-European J. Math.

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In this paper, we applied the adaptive grid Haar wavelet collocation method (AGH-WCM) for the numerical solution of parabolic partial differential equations (PDEs). The approach of AGHWCM for the numerical solution of parabolic PDEs is mentioned, the obtained numerical results, error analysis are presented in figures and tables. This shows that, the AGHWCM gives better accuracy than the HWCM and FDM. Some of the test problems are taken for demonstrating the validity and applicability of the AGHWCM.

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A Multilevel Wavelet Collocation Method for Solving Partial Differential Equations in a Finite Domain

Cited by 93 publications

References 0 publications

Three real‐space discretization techniques in electronic structure calculations

Three real‐space discretization techniques in electronic structure calculations

Adaptive interpolation wavelet and homotopy perturbation method for partial differential equations

Numerical solution of parabolic partial differential equations using adaptive gird Haar wavelet collocation method

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