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Haar wavelets method for solving Pocklington's integral equation

M. Shamsi, Mohsen Razzaghi, J. Nazarzadeh, Masoud Shafiee (2004)

Kybernetika

A simple and effective method based on Haar wavelets is proposed for the solution of Pocklington’s integral equation. The properties of Haar wavelets are first given. These wavelets are utilized to reduce the solution of Pocklington’s integral equation to the solution of algebraic equations. In order to save memory and computation time, we apply a threshold procedure to obtain sparse algebraic equations. Through numerical examples, performance of the present method is investigated concerning the...

Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

Markus Bachmayr (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed....

Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

Markus Bachmayr (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...

Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

Markus Bachmayr (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...

Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

Markus Bachmayr (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed....

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