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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: Theoretical analysis of the generalized finite difference methodInfluential work since 2022
- Pick up a classic book: Finite Difference Methods in Financial EngineeringThe most-reprinted book on the subject
- Read the landmark paper: Mimetic finite difference methodCited 433 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)
Mimetic finite difference method
3D finite-difference method using discontinuous grids
Hybrid finite difference/finite element immersed boundary method
Nonstandard finite difference method by nonlocal approximation
A finite-difference contrast source inversion method
Finite difference method for generalized Zakharov equations
Elastic finite-difference method for irregular grids
Slow-wave finite-difference beam propagation method
🆕 Influential since 2022
Theoretical analysis of the generalized finite difference method
On the nonstandard finite difference method for reaction–diffusion models
Difference finite element method for the 3D steady Stokes equations
A nodal immersed finite element-finite difference method
Finite Difference–Collocation Method for the Generalized Fractional Diffusion Equation
📚 Books worth reading
Finite Difference Methods in Financial EngineeringDaniel J. Duffy · 2006- 📕Finite-difference migration by optimized one-way equationsMyung W. Lee · 1985
- 📕A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equationsAmir Yeffet · 1999
Introduction to groundwater modelingHerbert F. Wang, Mary P. Anderson · 1982- 📕Wing-body aeroelasticity on parallel computersChansup Byun · 1996
Numerical Partial Differential EquationsJ. W. Thomas · 2010
Finite difference methods on irregular networksBernd Heinrich · 1987
Computational electrodynamicsAllen Taflove · 1995
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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