What is Difference: Definition and 1000 Discussions

A finite difference is a mathematical expression of the form f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems.
Certain recurrence relations can be written as difference equations by replacing iteration notation with finite differences.
Today, the term "finite difference" is often taken as synonymous with finite difference approximations of derivatives, especially in the context of numerical methods. Finite difference approximations are finite difference quotients in the terminology employed above.
Finite differences were introduced by Brook Taylor in 1715 and have also been studied as abstract self-standing mathematical objects in works by George Boole (1860), L. M. Milne-Thomson (1933), and Károly Jordan (1939). Finite differences trace their origins back to one of Jost Bürgi's algorithms (c. 1592) and work by others including Isaac Newton. The formal calculus of finite differences can be viewed as an alternative to the calculus of infinitesimals.

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  1. A

    I Solving Poisson's Equation Using Finite Difference

    I am using the Finite Difference Method to solve Poisson's equation \frac{\partial \phi}{\partial z^2} = \frac{\rho}{\epsilon} To do it is discretized according to the Finite Difference Approximation of the second order derivative yielding the following set of equations for each grid point...
  2. S

    B Phase Diff: Why Does 180° Change Occur?

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  3. F

    I Difference between global and local gauge symmetries

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  4. streeters

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  5. E

    Difference in hues between eyes

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  6. J

    I Newton Divided Difference Interpolation Polynomial

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  7. fuvest

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  8. M

    I Difference between 1-form and gradient

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  9. Asmaa Mohammad

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  10. J

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  11. Mr Davis 97

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  12. nagyn

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  13. N

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  14. N

    Difference in flight time for two planes with different velocity profiles

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  15. kolleamm

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  16. H

    Need help understanding potential difference practically

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  17. F

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  18. Benjamin Crump

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  19. T

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  21. ShayanJ

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  22. CricK0es

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  23. J

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  24. M

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  25. T

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  26. F

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  27. A

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  28. P

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  29. B

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  30. PhiowPhi

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  31. Shardul Khare

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  32. donaldparida

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  33. G

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  34. donaldparida

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  35. F

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  36. Const@ntine

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  37. Vitani11

    I What is the difference between these two approaches?

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  38. K

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  39. FQVBSina

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  40. S

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  41. M

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  42. F

    MHB Cartesian product and symmetric difference

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  43. pellman

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  44. G

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  45. Mr Davis 97

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  46. O

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  47. N

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  48. ChloeYip

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  49. B

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  50. S

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