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Finite difference

About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.


Papers
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Journal ArticleDOI
TL;DR: In this paper, a method for constructing boundary conditions (numerical and physical) of the required accuracy for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems is presented.

728 citations

Book
28 Mar 1988
TL;DR: In this article, a comprehensive presentation of numerical methods suitable for the analysis of various heat transverse and fluid flow problems that occur in research, practice, and university instruction is given.
Abstract: A comprehensive presentation is given of virtually all numerical methods that are suitable for the analysis of the various heat transverse and fluid flow problems that occur in research, practice, and university instruction. After reviewing basic methodologies, the following topics are covered: finite difference and finite element methods for parabolic, elliptic, and hyperbolic systems; a comparative appraisal of finite difference versus finite element methods; integral and integrodifferential systems; perturbation methods; Monte Carlo methods; finite analytic methods; moving boundary problems; inverse problems; graphical display methods; grid generation methods; and programing methods for supercomputers.

718 citations

Journal ArticleDOI
Bo Strand1
TL;DR: In this article, the authors presented a multi-parameter family of difference operators when τ⩾3, where τ is the dimension of the difference operator and λ is the number of points in the difference matrix.

703 citations

Book
01 Jan 1976
TL;DR: On Engineering By J T Oden J N Reddy ONLINE SHOPPING for NUMBER InTRODUCTION
Abstract: On Engineering By J T Oden J N Reddy ONLINE SHOPPING FOR NUMBER INTRODUCTION AN INTRODUCTION. MATHEMATICAL LEARNING THEORY R C ATKINSON. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF INVERSE. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF FINITE. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF WAVES. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF INVERSE. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF THE NAVIER. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF VIBRATIONS. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF INVERSE. INTRODUCTION MATHEMATICAL THEORY FINITE ELEMENTS ABEBOOKS. AN INTRODUCTION TO THE MATHEMATICAL THEORY OF WAVES. AN INTRODUCTION TO THE

686 citations

Journal ArticleDOI
TL;DR: An efficient and accurate semianalytical method to map the molecular surface of a molecule onto a three‐dimensional lattice and a procedure that calculates induced surface charges from the FDPB solutions and then uses these charges in the calculation of reaction field energies.
Abstract: This article describes a number of algorithms that are designed to improve both the efficiency and accuracy of finite difference solutions to the Poisson-Boltzmann equation (the FDPB method) and to extend its range of application. The algorithms are incorporated in the DelPhi program. The first algorithm involves an efficient and accurate semianalytical method to map the molecular surface of a molecule onto a three-dimensional lattice. This method constitutes a significant improvement over existing methods in terms of its combination of speed and accuracy. The DelPhi program has also been expanded to allow the definition of geometrical objects such as spheres, cylinders, cones, and parallelepipeds, which can be used to describe a system that may also include a standard atomic level depiction of molecules. Each object can have a different dielectric constant and a different surface or volume charge distribution. The improved definition of the surface leads to increased precision in the numerical solutions of the PB equation that are obtained. A further improvement in the precision of solvation energy calculations is obtained from a procedure that calculates induced surface charges from the FDPB solutions and then uses these charges in the calculation of reaction field energies. The program allows for finite difference grids of large dimension; currently a maximum of 571 3 can be used on molecules containing several thousand atoms and charges. As described elsewhere, DelPhi can also treat mixed salt systems containing mono- and divalent ions and provide electrostatic free energies as defined by the nonlinear PB equation.

682 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023153
2022411
2021722
2020679
2019678
2018708