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.

View More On Wikipedia.org
Recent contents Top users
  1. T

    What is the difference between PP(polypropylene) and CPP?

    To my knowledge, CPP means cast-polypropylene, which I've seen used in a coaxial cable. Some cables use CPP as dielectric material. My question is: 1. what is the difference between PP(polypropylene) and CPP? 2. How is CPP made? 3. Is the permittivity and loss tangent of CPP different from that...
  2. SOUKRAT

    The difference between Draftsman and Designer

    Hi everyone Both Draftsman and Designer uses CAD Softwares what i want to know the difference between them according to 1- Educational level 2- Job Roles 3- maximum Promotion can get Thanks
  3. F

    What potential difference actually means

    Does potential difference only indicate how much energy each coulomb have, or make current flow, or do both?
  4. Kaneki123

    A Question about potential difference in Wire

    Okay...I got a question. Charges move in a wire due to an electric field across its ends. Now, positive test charge in an electric field would have higher electric potential nearer to the positive plate than anywhere else. Now in case of a circuit, like the one I have drawn, the electric...
  5. bhobba

    A Difference Between Covariance and Diffeomorphism Invarience

    Hi I have studied GR form a number of sources - my favorite being Wald - he uses Diffeomorphism Invarience, the rest General Covarience/Invarience. Wald is more mathematically sophisticated but at rock bottom is there really any difference. My suspicion is Wald does it because there is a...
  6. L

    Finding the sum and difference of two drag coefficients

    Homework Statement I have to determine the sum and difference of the two coefficients of drag between two individual items that make a torque AUT. I'm given the diameter of each bottle (6.35 cm), wind velocity (14.3 m/s), the forces of the lift load cells (+0.0741 N, -0.0741 N), and the force...
  7. F

    The difference between electric field and electrical charge

    what is difference between electric field and electrical charge?
  8. PeterDonis

    Insights The Fundamental Difference in Interpretations of Quantum Mechanics - Comments

    Greg Bernhardt submitted a new PF Insights post The Fundamental Difference in Interpretations of Quantum Mechanics Continue reading the Original PF Insights Post.
  9. Enelafoxa

    Confused about the difference method

    Homework Statement Use the diffence method to sum the series ##\sum_{n=2}^N\frac {2n-1}{2n^2(n-1)^2}## Homework Equations from the textbook by Riley i have ##S_N=\sum_{k=1}^m f(N-k+1)-\sum_{k=1}^m f(1-k)## The Attempt at a Solution I prefer to write it as ##S_N=\sum_{k=1}^m...
  10. S

    Potential difference in between positive and negative charge

    Homework Statement Two point charges Q1= +5.00 nC and Q2 = -3.00 nC are separated by 35.0cm. What is the electric potential at a point midway between the charges? Homework Equations V = Ke(q/r), PE = Vq[/B] The Attempt at a Solution This question is from Serway textbook. The answer is...
  11. S

    Difference between chemical physics and physical chemistry

    What is the difference between physical chemistry and chemical physics?
  12. K

    Pressure Difference: F=10 Tonnes, A=100 sq m - Calculate & Understand

    Homework Statement [/B] A ceiling can blow off due to pressure difference between the inside and outside of the house. In a magazine, it said: "Let's have a ceiling of 100 square meters. A pressure difference of 1% of the air pressure between the two sides of the ceiling is equivalent to a lift...
  13. Abhimessi10

    Difference between relative velocity and effective velocity

    Can anyone tell me the difference between concept of relative velocity and effective velocity and when to use the concept of relative velocity? For example, if a guy throws a ball from a moving object at an angle theta it undergoes projectile motion we write horizontal velocity as...
  14. entropy1

    I What is the difference between cfd and realism?

    What is the difference between counterfactual definiteness on one side and realism on the other? And what are their definitions? (references will be welcome if given).
  15. K

    Diagram about potential difference over current

    Homework Statement [/B]Homework Equations [/B] I = G * U The Attempt at a Solution [/B] Hello, i know the solution is 5.0 A/V but i don't know if my way of solving this was correct. I rearranged it to G= I/U and solved this equation for all the values in the table and then added them...
  16. Jayalk97

    Difference between h-parameters and hybrid pi?

    Hey guys, I'm confused as to the difference between the h-parameters usually given by datasheets and their hybrid-pi model analogues. For instance, I know hfe = Beta in small signal analysis, but what about the other h-parameters. Thanks for any help with clarifying this.
  17. K

    B Postulates and pseudoscientific hypothesis difference?

    A postulate is a statement that is taken to be true, to serve as a premise or starting point for further theories. (e.g. Bohr's postulates) Hypothesis is a theory which can after testing be accepted or rejected. But a postulate is something that is assumed to be true without proof. Among other...
  18. M

    I Velocity difference not preserved in special relativity

    Consider single line motion. If an observer sees two objects, and one is seen moving say 50 m/s faster than the other, will all other observers measure the same velocity difference? The answer seems to be 'No' from the velocity addition formula of special relativity? Thus same velocity...
  19. S

    Difference between bifurcation and chaos

    Chaos is when the waveforms become aperiodic. I think bifurcation is the phenomenon inclusive of chaos and in addition, it is also termed for situations in which the waveforms become n-periodic.Does bifurcation include period-n phenomenon as well as chaos? From period-n it means that still the...
  20. A

    External Forces and Potential Difference

    Homework Statement The work done by an external force to move a -8.0 uC charge from point a to point b is 25*10^-4 Joules. If the charge was started from rest and had 5.2 * 10^-4 Joules of kinetic energy when it reached point b, what must be the potential difference between a and b? Homework...
  21. C

    Potential difference in multi cell circuit

    Homework Statement Find potential difference between a and b in the figure Homework Equations Q=cv The Attempt at a Solution can anybody tell me how to apply the equation in this problem with more than one cell [/B]
  22. Fodder

    I Does the open area of my window make a difference?

    So I was wondering whether the amount of open area of my window would make a difference in how much cold air gets in? Please tell me if I should provide more information, I'm pretty new to this.
  23. JTC

    Difference between Hamiltonian and Lagrangian Mechanics

    Hello, I am trying to "integrate into my understanding" the difference between Hamiltonian and Lagrangian mechanics. In a nutshell: If Lagrange did all the work and formulated L = T - V, they why is Hamilton's name attached to the minimization principle? YES; I KNOW about Hamilton's Second...
  24. Rachana Malik

    Programs Difference Between B.Tech and MCA

    What is the difference between B.Tech on CS and MCA??
  25. L

    A Convergence order of central finite difference scheme

    For example, when we solve simple 1D Poisson equation by finite difference method, why three point central difference scheme on uniform grid (attached image) is second order method for solution convergence? I understand why approximation of first derivative is second order (and that second...
  26. A

    Is there a difference between work and circulation?

    These two things seem to be exactly the same (even down to the same formula), so I'm having difficulty understanding why they are two different terms. Is circulation just the work done as you go around a circle once?
  27. S

    I Difference between oscillatory/cyclic model and big bounce?

    If a Big Bounce can occur "after a universal singularity is reached or a repulsive quantum force causes re-expansion" then what differentiates it from oscillatory/cyclic models if both of them defend that the universe will re-expand from a singularity or before that...
  28. M

    A Is the discretization for the PDE correct?

    Hi PF! I'm trying to finite difference a FTCS PDE $$h_t+\partial_x\left[h^3(h_{xxx}+(Kf'(h)-G)h_x\right] = 0$$ where ##K## and ##G## are constants. ##f'(h) = -(n(h^*/h)^n-m(h^*/h)^m)/h##. Boundary conditions are ##h_x=h_{xxx}=0## at both ends of the ##x## domain (however long you want to make...
  29. W

    QM: Difference between these Initial Wavefunctions

    Homework Statement I've been asked as a part of some school project to find the Fourier transform, and time evolution of the following initial wavefunctions: 1. ##\Psi(x,0) = Ae^{\frac{-x^2}{2\sigma ^2}}## 2. ##\Psi(x,0) = Be^{\frac{-x^2}{2\sigma ^2}}e^{\frac{ipx}{\hbar}}## What physical...
  30. ISamson

    Difference between Analog and Digital Pins on my Arduino Board

    I wanted to ask what the difference between analog and digital pins is on my Arduino (or any other board). I have been using both but don't really know what the difference is. Thanks!
  31. S

    I What is the difference between phase space and state-space?

    In state space, the coordinates are the state variables of a system.So,each point in state space represents a specific value of state variables.Thus,state space representation represents the changes in a dynamical system. The state variables are the minimum number of variables which uniquely...
  32. V

    Difference between charge and charge density

    So I am studying Gauss's law and I am a bit confused about something. If I am asked to compute the volume or surface charge density of a solid perfectly conducing sphere with a charge Q and radius r, what is being asked of me? Am I just being asked to compute the volume of a sphere and multiply...
  33. M

    A Better way to find Finite Difference

    Given a function ##\psi## having ##N## components, how would you (as fast as possible) construct ##\psi'## also having ##N## components? I thought about taking a forward finite difference approach on the first ##N-1## components of ##\psi## to generate ##\psi'## and then a backward finite...
  34. T

    A Difference between virtual displacement and differential?

    What exactly is the difference between a virtual displacement and a differential displacement? It seems like they are really the same thing if by differential we assume we are talking about a distance whose magnitude approaches zero.
  35. H

    I Difference between CHSH and Bell inequalities

    Bell's Inequality, P(a,b)-P(a,d)+P(c,b)+P(c,d) is calculated as: S = a*b - a*d + c*b + c*d <= 2. It is valid for all values of a, b, c and d between -1 and +1 It is also valid for counts, a=a's counts/total counts of a,b,c &d. b, c,and d are derived similarly. Negative counts are not allowed...
  36. D

    Difference between Ultrasonic waves and sound waves.

    Hello everyone, Can I seek help on the difference of ultrasonic waves and sound waves? I find it confusing.
  37. S

    B What is difference between platenary core, mantle & crust?

    There seems to be a standard way of looking at the composition of planets, and am curious as to why one region is called the core and then something above that is the mantle, and then finally the crust. It seems that the core is metallic, but what exactly defines the mantle & crust. I was...
  38. X

    Determining the distance difference of towers of a bridge

    Homework Statement Huge suspension bridges are build with the Earth's roundness in mind. The two towers are plumb line straight up and down and yet, because of their colossal size, they are a bit further apart at their tops than they are at their base. So, how can we calculate what this...
  39. sams

    A Difference between conduction & convection current density?

    Hello Everyone, Could anyone please explain the difference between the conduction current density (J=σE) and the convection current density (J=ρvd)? I really appreciate any examples or applications to further elaborate these two theories. Note: vd is the particles' average drift velocity...
  40. Moayd Shagaf

    I Difference Between d3x and triple Integral

    So My Question Is Simple, But It confuse me too much! What Is Difference between the notation ∫d3x and ∫∫∫dxdydz ?
  41. M

    Strength of electric field given potential difference

    Homework Statement What is the strength of the electric field between two parallel conducting plates separated by 1.00 cm and having a potential difference (voltage) between them of 1.50×104 V? Homework Equations ΔV = qΔU ΔV = -∫E⋅dl E = kq/r2 The Attempt at a Solution I am not sure where to...
  42. D

    Factoring Involving the Difference of Two Squares

    Homework Statement Completely factor: $$5abc^4-80ab$$ Homework Equations N/A The Attempt at a Solution $$5abc^4-80ab$$ $$5ab\left(c^4-16\right)$$ $$5ab\left(c^2+4\right)\left(c^2-4\right)$$ [/B] The correct solution is ##5ab\left(c^2+4\right)\left(c+2\right)\left(c-2\right)## I can see...
  43. A

    I Difference between transient and steady state solution

    In driven SHM, we ignore an entire section of the solution to the differential equation claiming that it disappears once the system reaches a steady state. Can someone elaborate on this?
  44. A

    I Difference between binding energy and ionization energy

    Hi! I wonder since some time why ionization energies are not equal to binding energies. For instance, take the case of aluminum in the following configuration [Ne]3s²3p Ionization energy ~ 6 eV Binding energy ~ 5 eV Where does this difference come from ? Thanks in advance
  45. deuel18

    Difference in power transfer with gear location

    I'd like to know if there's a power transfer loss depending on how gears are connected and placed relative to each other. For the two distinct image down below, imagine ALL GEARS HAVE EXACTLY THE SAME DIAMETERS and the setup is such that the viewers are seeing the top (aerial view) and the gears...
  46. S

    Potential difference across capacitor in a network

    Homework Statement Determine the potential difference across the plates of the capacitor of the network shown in the figure. Homework Equations kirchoff's loop rule q=vc 3. The attempt at a solutio applying kirchhoffs law starting at bottom right point, q/c2-E1+q/c1+E2=0 =>E2-E1=-q/c1-q/c2...
  47. PrathameshR

    B Difference between zero and identically zero

    What's the difference between something (eg a function or a matrix) becoming zero and it becoming identically zero? Illustrations will be helpful. Thanks
  48. H

    A Finite difference of fourth order partial differential

    What is a finite difference discretization for the fourth-order partial differential terms \frac{\partial u}{\partial x}k\frac{\partial u}{\partial x}\frac{\partial u}{\partial x}k(x,y)\frac{\partial u}{\partial x} and \frac{\partial u}{\partial x}k(x,y) \frac{\partial u}{\partial y}...
  49. S

    I Difference between vectors and one-forms

    Hello! I am reading some introductory differential geometry and they define the vector space associated to a point of a manifold as the tangent plane at that point. Intuitively it makes sense to call these vectors (just as the speed is the tangent to the trajectory), but why are those called...
  50. J

    Intro Physics Difference between University Physics 13th and 14th edition?

    Hi, I'd like to ask if anyone knows the differences between the 13th and 14th editions of University Physics by Young and Freedman? I have a copy of the 13th edition but a friend is taking a class using the 14th edition and he is considering borrowing mine or getting a new copy. Thanks in advance!
Back
Top