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, a biphasic continuum description is used to represent the soft tissue as a two-phase mixture of incompressible inviscid fluid and a hyperelastic, transversely isotropic solid.
122 citations
TL;DR: In this article, a second order accurate finite difference method is presented for solving two-dimensional variable coefficient elliptic equations on Cartesian grids, in which the coefficients, the source term, the solution and its derivatives may be nonsmooth or discontinuous across an interface.
122 citations
TL;DR: In this article, a modified equation analysis was used to develop formally fourth order accurate finite difference and pseudospectral methods for the one-dimensional wave equation, which can be used to achieve fourth order time accuracy with no increase in storage.
Abstract: In this paper we use a modified equation analysis to develop formally fourth order accurate finite difference and pseudospectral methods for the one-dimensional wave equation. The difference scheme is constructed by performing a modified equation analysis of a centered, second-order conservative scheme to determine its dominant error term. Subtracting a centered discretization of this term from the scheme cancels the second order truncation errors. This technique yields a formally fourth order accurate explicit difference scheme that employs only three time levels. Similarly, the modified equation technique can be used to achieve fourth order time accuracy for the pseudospectral method with no increase in storage. The difference and pseudospectral schemes are fourth order convergent for constant coefficients even when a spatially singular forcing term is used for a source. Numerical results are given comparing the accuracy and efficiency of these methods for some model problems. Finally, we present a gene...
122 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |