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Everything about Finite difference

Discrete analog of a derivative

A finite difference is a mathematical expression of the form f(x + b) − f(x + a). Finite differences (or the associated difference quotients) are often used as approximations of derivatives, such as in numerical differentiation. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Finite differenceA 5-minute orientation
  2. Skim a recent paper: Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equationsInfluential work since 2022
  3. Pick up a classic book: Electromagnetic Simulation Using the FDTD MethodThe most-reprinted book on the subject
  4. Read the landmark paper: Compact finite difference schemes with spectral-like resolutionCited 5,540 times
  5. Go sideways: Finite difference methodA closely related topic
  6. Go sideways: Umbral calculusA closely related topic

📖 Definitions

Noun A difference between the value of a function evaluated at a number, and the value of the same function evaluated at a different number, a fixed distance from the first.

🗂️ The subject at a glance

  1. Basic types
  2. Relation with derivatives
  3. Higher-order differences
  4. Polynomials
  5. Arbitrarily sized kernels
  6. In differential equations
  7. Newton's series
  8. Calculus of finite differences
  9. Generalizations
  10. Multivariate finite differences

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics