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
1 / 2
Papers
TL;DR: A Symmetrical Conservative Metric Method (SCMM) is newly proposed based on the discussions of the metrics and Jacobian in FDM from geometry viewpoint by following the concept of vectorized surface and cell volume in Finite Volume Methods (FVMs).
111 citations
TL;DR: In this article, stability estimates and convergence analysis of finite difference methods for the Biot's consolidation model are presented, and central differences for space discretization and a weighed two-level time scheme are analyzed.
111 citations
TL;DR: In this article, a new numerical technique for solving the fractional order diffusion equation is introduced, which basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method.
Abstract: In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton’s iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.
111 citations
Book•
1 Jan 2007
TL;DR: In this paper, the authors introduce mathematical modelling and numerical simulation, and present a review of Hilbert spaces, finite difference method, finite element method, and infinite difference method for matrix numerical analysis.
Abstract: 1. Introduction to mathematical modelling and numerical simulation 2. Finite difference method 3. Variational formulation of elliptic problems 4. Sobolev spaces 5. The mathematical study of elliptical problems 6. The finite element method 7. Eigenvalue problems 8. Evolution problems 9. Introduction to optimization 10. Optimality conditions and algorithms 11. Methods of operational research APPENDICES 12. Review of Hilbert spaces 13. Matrix numerical analysis Bibliography Index
111 citations
TL;DR: In this article, the fast Karhunen-Loeve transform is extended to images with nonseparable or nearly isotropic covariance functions, or both, for image restoration, data compression, edge detection, image synthesis, etc.
Abstract: Stochastic representation of discrete images by partial differential equation operators is considered. It is shown that these representations can fit random images, with nonseparable, isotropic covariance functions, better than other common covariance models. Application of these models in image restoration, data compression, edge detection, image synthesis, etc., is possible. Different representations based on classification of partial differential equations are considered. Examples on different images show the advantages of using these representations. The previously introduced notion of fast Karhunen-Loeve transform is extended to images with nonseparable or nearly isotropic covariance functions, or both.
110 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |