Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
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Papers
TL;DR: In this article, higher-order Pade approximations are applied to derive accurate and stable parabolic equations for sound propagation in oceans bounded below by an elastic bottom or bounded above by ice cover.
Abstract: Higher-order Pade approximations are applied to derive accurate and stable parabolic equations for sound propagation in oceans bounded below by an elastic bottom or bounded above by ice cover. Accuracy is achieved by placing constraints on the derivatives of the Pade approximations at the point corresponding to the reference wave number. Stability is achieved by requiring that the Pade approximations map part of the lower-left quadrant of the complex plane into the upper half of the complex plane. Elastic parabolic equations based on these Pade series can handle problems involving compressional, shear, and interface waves, very wide propagation angles, and large depth variations and weak range variations in the seismoacoustic parameters. A finite-difference spectral solution is developed for generating reference solutions and starting fields. The rotated elastic parabolic equation is used to investigate the accuracy of the elastic parabolic equation for range-dependent problems.
135 citations
01 Apr 1967-Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics
TL;DR: In this paper, the authors describe a lion which is a ppli cable when s impl e rec urrence proce dures ca nnol be used becau se uf in sla bilil Y.
Abstract: A ne w al~orilhm is ~ive n fur cumpulin ~ Ihe soluliun of a ny secu nd-orde r lin ea r diffe re nce e qua lion which is a ppli cable when s impl e rec urrence proce dures ca nnol be used becau se uf in sla bilil Y. Co mpare d wilh Ih e we ll -knuwn lV1ill e r a l ~o rilhm Ih e ne w m elhod has Ih e advanla~es of (i) a Ul umal ic ally deLermining the currec t number of rec urrence steps. (ii ) app lying to illllOlllo~en eou s differe nce eqlla ~ li uns, (iii ) e nab lin g mure powerful e rrur a na lyses lu be co ns lru c led. The me lhud is illuSlra led by num e rica l comp ulalion s, ineludin~ e rror ana lyses. uf A n~e rWe be r . S iruve, a nd Besse l fun c li uns, and Ih e s u luli un of a differe nli a l e qualiun in C he bys he v se ri es.
134 citations
TL;DR: In this article, a similarity transformation is used to transform the constitutive equations into a system of nonlinear ordinary differential equations, and the resultant system of equations is then solved numerically using implicit finite difference method.
134 citations
13 Jul 1983
134 citations
TL;DR: In this article, two cell-centered finite difference schemes on Voronoi meshes are derived and investigated, and the stability and error estimates in a discrete H1-norm for both symmetric and nonsymmetric problems, including convection dominated, are proven.
Abstract: Two cell-centered finite difference schemes on Voronoi meshes are derived and investigated. Stability and error estimates in a discrete H1-norm for both symmetric and nonsymmetric problems, including convection dominated, are proven. The theoretical results are illustrated with several numerical experiments. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:193–212, 1998
134 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |