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Everything about Finite difference method
Class of numerical techniques
In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time domain are discretized, or broken into a finite number of intervals, and the values of the solution at the end points of the intervals are approximated by solving algebraic equations containing finite differences and values from nearby points. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Finite difference methodA 5-minute orientation
- Skim a recent paper: An immersed finite element material point (IFEMP) method for free surface fluid–structure interaction problemsInfluential work since 2022
- Pick up a classic book: Drag reduction on circular cylinders by ejecting jet from rear stagnation regionThe most-reprinted book on the subject
- Read the landmark paper: A finite point method for elasticity problemsCited 157 times
- Go sideways: Finite differenceA closely related topic
- Go sideways: Numerical differentiationA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
A finite point method for elasticity problems
An explicit material point finite element method for hyper‐velocity impact
Coupling of finite element method with material point method by local multi-mesh contact method
A finite point method for compressible flow
Error estimates for the finite point method
A finite point method for incompressible flow problems
Simple modifications for stabilization of the finite point method
Radial point interpolation based finite difference method for mechanics problems
🆕 Influential since 2022
An immersed finite element material point (IFEMP) method for free surface fluid–structure interaction problems
American options pricing under regime-switching jump-diffusion models with meshfree finite point method
A finite point method for the fractional cable equation using meshless smoothed gradients
An adaptive tailored finite point method for the generalized Burgers’ equations
Sequential Hybrid Finite Element and Material Point Method to Simulate Slope Failures
📚 Books worth reading
- 📕Drag reduction on circular cylinders by ejecting jet from rear stagnation regionS. Atsuchi · 1997
- 📕Discretized energy minimization in a waveguide with point sourcesG. Probst · 1994
- 📕Algorithmic arithmetic, geometry, and coding theoryInternational Conference Arithmetic, Geometry, Cryptography and Coding Theory (14th 2013 Marseille, France) · 2015
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Finite element method Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical…
- Numerical methods for ordinary differential equations Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations…