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

    A 2D Finite Difference Convergence Rate Issues

    I have completed a 2D finite difference code in MATLAB that has a domain of (0,1)x(0,1) and has Dirichlet Boundary Conditions of value zero along the boundary. I get convergence rates of 2 for second order and 4 for fourth order. My issue now is that I'm now wanting to change the domain to a...
  2. O

    Difference between instantaneous velocity and acceleration

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  3. S

    Difference between probability waves & electromagnetic waves?

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  4. Kuzon

    What is the difference btwn positive and negative electrodes

    I'm so confused, is the voltage reading of the meter gathered by: positive electrode charge - negative electrode charge = potential difference I don't get why there is a positive and negative electrode and what they do
  5. H

    MHB Pinewood derby with a slight difference

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  6. L

    Potential difference between two points

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  7. TheBigDig

    Engineering Finding Phase Difference in an RC circuit

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  8. chandrahas

    Difference between a tokamak and a spherical tokamak

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  9. P

    MHB Can Anyone Solve This Difference Equation Using Generating Functions?

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  10. D

    Finding the transfer function for a difference amplifier

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  11. Ned Taylor

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  12. D

    I Time Difference on a quantum level

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  13. haushofer

    A Chaos: difference vs differential equation

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  14. qnach

    I Chirality/Helicity difference?

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  15. F

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  16. T

    I Difference of resonant and non-resonant neutrino oscillation

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  17. Archie Medes

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  18. M

    MHB Which method is easier and why?

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  19. Vitani11

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  20. N

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  21. E

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  22. R

    What is the difference between monohybrid and dihybrid cross

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  23. thenewmans

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  24. Irfan Nafi

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  25. Riverbirdy

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  26. M

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  27. Tyler R

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  28. Theudius

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  29. Shardul Khare

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  30. A

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  31. Y

    MHB Is the Symmetric Difference Problem Solved?

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  32. Vitani11

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  33. G

    Neutral potential ground difference

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  34. D

    A Difference Between Outer and Tensor

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  35. J

    I Difference between statistical and dynamical properties

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  36. F

    Newton interpolary difference formula

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  37. Adgorn

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  38. D.B.SriHridai

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  39. ElPimiento

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  40. R

    Difference between vibrational, rotational and electron temperature

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  41. M

    Difference Electric Field Strength Point Charges vs. Plates

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  42. T

    Why's Potential Difference Different in Series Capacitors?

    My book says "the magnitude of charge on all plates in a series connection is the same." It then says "potential differences of the individual capacitors are not the same unless their individual capacitances are the same." If the plates were all the same size, given that they all have equal...
  43. Farang

    Calculating pressure / energy difference confusion

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  44. ItsTheSebbe

    I Difference Analysis and Calculus

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  45. G

    I Difference between "realistic" and "predetermined"

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  46. S

    Why is Newton's Ring Dark in the Center? Exploring Path Difference Theory

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  47. S

    What's the difference between series an parallel components in the pictures

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  48. jlmccart03

    How Does Charge Movement Affect Electric Potential and Kinetic Energy?

    Homework Statement Two charged rods, each with net charge -Q0 are held in place as shown in the top view diagram below. a. A small test charge -q0 travels from point X to point Y along the circular arc shown. i. Draw an arrow on the diagram at each point to show the direction of the electric...
  49. theideasmith

    Difference in potential energy of two charge configurations

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  50. M

    Heat Transfer, Finite difference, Curved geometry

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