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. B

    What is the difference between DIN 915 and DIN 916 set screws?

    What is the difference between "Hexagon socket set screw with dog point DIN 915" and "Hexagon socket set screws with cup point DIN 916" about usage field?
  2. T

    Percentage difference problem

    See the question : https://www.thestudentroom.co.uk/att...hmentid=978958 The mark scheme/answer : https://www.thestudentroom.co.uk/att...hmentid=978956 I have got the answer to the vertical height gained = 1.355 m. No problem. But not the value of the percentage difference. Their value : 23%...
  3. S

    B What is the difference between writing f and f(x)?

    Some people say f is the function and some say f(x) is the function. f and f(x) are often used interchangeably. I have seen in many textbooks, sentences such as "Let f(x) be a function ...". But as we know that f represents our function then why it is given "f(x) is a function". i am confused...
  4. D

    A Numerical Hartree Fock with Finite Difference Matrices for Helium

    Here is the paper again: https://www.mdpi.com/2218-2004/6/2/22?type=check_update&version=2#related_content For a class project I need to calculate the energy levels of atoms using the Hartree Fock method as presented in this paper which essentially brute forces the calculation using finite...
  5. eleanorwest83

    Pressure relief valves & pressure regulators - What's the difference?

    What is the difference between a pressure reducing valve and a pressure relief valve? pressure-reducing/regulating/ relief/release - There are so many different options available! I read this article on Fluid Controls that did a really good job of explaining pressure regulators, but I am a bit...
  6. S

    B What is the Difference between imaginary part and imaginary number?

    I am a high school student and I have a doubt regarding Complex Numbers. when we define a complex number we say that a number of the form z=a+ib ,where a and b are real numbers is called a complex number. a is called the real part and b is called the imaginary part, but I have a doubt here we...
  7. M

    I Why is the mass of the singlet meson higher than the octet mesons in QCD?

    Hello! I am reading some group theory applied to QCD and they show how by using the lightest 3 quarks in the ##l=0## state we get 9 pseudoscalar mesons and 9 vector mesons. The difference in masses between the 2 classes is explained by the existence of a spin-spin interaction, which seems like a...
  8. greg_rack

    B Difference between RC and RRC circuits

    Circuit A(RC) Circuit B(RRC) Hi guys, the thing I don't get is why the maximum charge of the A capacitor is ##q_{0}=C\cdot EMF## whilst in the other case you must consider the drop in tension caused by the first resistor, so the maximum charge of the cap is ##q_{0}=C\cdot (EMF-V_{R1})##. Aren't...
  9. P

    Why does roofing occur despite the difference in chemical shift?

    J is 7.2 and 7.1 for the triplets (7.2 for the pentet, 7.1 for the sextet), chemical shift 0.93 and 2.62Also is it a AMSX or AMX spinsystem?
  10. greg_rack

    Final electric potential difference in a circuit with two capacitors

    So, each capacitor must have a different potential difference, given by its capacity and charge... this would cause charge and current accordingly to flow in the circuit. But how do I determine the final potential difference, which would of course be the same for both of them? I have tried...
  11. Mircro

    Radio waves in air and water - difference in path

    Hello, this is an assigment form the 4th grade high school physics in Croatia, concerning electromagnetic waves. Radio waves of wavelength 12m propagate from the source. The source is on the surface of the water and two waves propagate from it: one through the air and the other through the...
  12. greg_rack

    Electric potential difference at the ends of a resistor

    So, having two parallel resistor ##R_{1}## and ##R_{2}## , the current flowing through the equivalent one will be ##I_{eq}=I_{1}+I_{2}##. Now, it comes the point I'm not totally getting: why is ##V_{eq}=V_{1}=V_{2}##? These V's are the difference of potential measured between which points...
  13. W

    B Difference between an Einstein frame and a String frame?

    I have listening to talks come across the terms"Einstein frame" and "String frame" but am not at all clear what they mean. Can anyone give a layman's explanation as to what is theses phrases mean in the context of cosmology ?
  14. M

    Programs Is there a difference between undergrad physics programs?

    My son is a high school senior applying to a mix of large public (two in-state and one out-of-state) universities, a couple mid-size selective private universities and one Ivy-league university. His intended major is physics (doesn't know what specialty although he visited Fermi Labs and is...
  15. F

    Engineering Difference between the carry flag and overflow flag

    Here's my explanation with an example: (d: decimal ) 7d + 2d = 9 d If signed: the result indicates an overflow, because it exceeds the maximum which is +7. ( 0111 + 0010 = 1001 ) However, CF = 0 indicating that there is no overflow which is wrong. OF = 0 ⊕ 1 = 1 -> invalid result, because the...
  16. greg_rack

    Clarifications about electric potential and potential difference

    Specifically, I haven't really got all the "methods" through which you could calculate or derive the electric potential and in some situations, I cannot understand how and when to apply this concept. Is it something caused by any charge, or must there be an interaction between the two to...
  17. F

    Boiling & Critical Temperature: Understanding The Difference

    Are boiling temperature and critical temperature the same or they are different things?
  18. Adams2020

    Mass difference due to electrical potential energy

    I do not really know the relationship between potential energy and mass difference. Isn't the difference in mass of protons and neutrons due to their quarks? (the neutron is made of two down quarks and an up quark and the proton of two up quarks and a down quark.) Please help.
  19. Y

    Programs Difference Between Postbaccalaureate and a Graduate Certificate?

    What'd the difference between a Postbaccalaureate and a Graduate Certificate? Is it possible to get a Postbaccalaureate in engineering? I can't find a university that offer a Postbaccalaureate in engineering, but plenty of schools that offer a Graduate Certificate in engineering.
  20. danielhaish

    Why can't two laser beams from two sources Interfere if they have a difference phase?

    I read in the internet that the reason that two laser can't Interference because they most likely have difference phase. but electromagnetic wave are just change in the electromagnetic filed that goes up and down , so mathematically they may Interference little let say that the there is...
  21. jaumzaum

    B What is the difference between "Unitless" and "Dimensionless"?

    Hello! I'm having trouble to understand the difference between unitless and dimensionless. Many people on the internet says different things, so I need someone to really confirm me this, because I'm turning crazy kkkk. So, let's start with temperature. I say T =400 K. 1) What is 400? Is it the...
  22. AN630078

    Difference in Gravitational Potential on the Moon

    1. Since the gravitaional field strength is 1/6 of that on Earth: W=mg W=90*9.81/6 W=90*1.635 W=147.15 ~ 147 N 2. ∆Ep=mg∆h ∆Ep=90*1.635*50 ∆Ep=7357.5 J I do not now whether this method would be suitable and if I should have instead used the formula for gravitaional Potential, V grav=-Gm/r? 3...
  23. Elias_HH

    Engineering What is the difference equation of the system?

    Hey guys, what is the difference equation of the signl seen in the figure ? my suggestion is: y(k) = 2u(k) + 2u(k-1) + 2u(k-2) - y(k-6)
  24. LCSphysicist

    Standing waves on a string -- Find the difference of phases

    The immediate thing i did here is ## \Delta \varphi = k(\Delta x) ## Interesting enough for a topic, if you use this equation you end up wrong like me, the answer is not D. Not sure what is the problem.
  25. B

    Finding the potential difference of a diode

    I've tried doing it but i haven't been able to find the resistance of the diode.
  26. Like Tony Stark

    Difference between curvilinear and rotational motion

    The solution states that there's no rotational motion when ##C## is cut (the motion is curvilinear), so we can take torques with respect to the centre of mass of the plate. But, isn't it rotating? I think of it as a pendulum, which describes a circular motion. What's the difference? Wouldn't the...
  27. bilzebor

    A Difference between generations of quarks

    hello, in the model of quarks, each of them is described by a flavor, but the quantum number for the first generation of quarks is the same (the isospin) for the up (1/2) and down (-1/2) quark. For the other generation though it is a distinct number (s,charm,...) for each quark. From what I...
  28. danielhaish

    Do two light waves with difference frequencies connect when they meet?

    for example the blue light wave have frequency of about 450Thz and the yellow wave have frequency of about 508thz (I found this data in the internet) , so if this two wave would get closer to each other we would observe them as green wave which have frequency of 526Thz . so my question is...
  29. Eclair_de_XII

    LaTeX What is the difference between a macro with no arguments and a name?

    This is some sample code that I drew up. The name is "\PFlink" The macro is "\linktoPF" My question is this: Would you be able to tell which is the name and which is the macro without referring to their respective definitions in the pre-amble below? \documentclass{article}...
  30. L

    Light interacting with Matter -- Does the wavelength make a difference?

    I heard somewhere that light in the visible spectrum that we see interacts with matter the most? Is that true, and in what ways?
  31. Kaushik

    Understanding the Phase Difference Between Voltage & Current in a Circuit

    Consider a circuit with a witch, capacitor and an AC voltage source. The sinusoidal AC voltage source is depicted in the following graph: We know that, ##Q = CV## ##\frac{dQ}{dt} = C \frac{dV}{dt}## ##i = C\frac{dV}{dt} \tag{1}## So from the graph, the voltage increases rapidly around ## t =...
  32. S

    A What is the difference between aggregation, nucleation and growth?

    Im bit confused about what is exactly the difference between the terms, which process every term describes ?
  33. P

    Difference in these two concepts of Magnetic Torque

    I am confused with the concept of Torque handled differently in books, Concept1: If a loop is placed in a magnetic field and the current flowing in the loop is ##I## there will be force and torque acting on the loop given by ##F = I \vec l \times \vec B ##. The torque is given by ##\tau =\vec...
  34. J

    Difference between abstraction layers and modularisation

    I understand abstraction to be the process of representing a system, concept or process in simple terms, leaving out finer details which may obfuscate the bigger picture. My understanding of layers of abstraction is that it refers to different depths of understanding of a concept where each...
  35. fresh_42

    Other Difference between Physics and Mathematics

    Our forums are full of physics and mathematics. One cannot talk about the former without getting into calculations and mathematics sooner or later: Hilbert spaces, differential operators and linear algebra all over the place. Students of both faculties have normally a similar motivation...
  36. thommy

    Why don't airplanes explode due to pressure difference?

    My question might sound trivial (I'm just a first year physics student anyways) , however I really feel the need to get an answer. Since the pressurized cabins inside an airplane are regulated at about 0.8 atm while the pressure outside doesn't surpass 0.2 atm (at 35 000+ ft of altitude)...
  37. J

    Reversible Otto Cycle Efficiency: Investigating the Difference from Carnot's

    So we know that every reversible engine working between the same temperatures will have the same efficiency(the same as Carnot engine). So let's consider for example reversible Otto cycle. So as you can see on the picture it is operating between ##T_1## and ##T_3##, so I was thinking that it...
  38. C

    Is there a difference between Faraday’s induction experiments?

    Faraday first demonstrated his law of induction by showing that when he created a current in one wire coil it created a second current in a second coil. Another experiment showed the same effect. When he moved a magnet through a wire coil, it created a current in the coil. My question is this...
  39. jaumzaum

    The REAL difference between a Galvanometer and an Ammeter

    Hello guys. I'm having some trouble to understand the real difference from the Galvanometer and the Ammeter. The best comment I saw in some forum was: Ammeter: ANY instrument used to measure electrical current Voltimeter: ANY instrument used to measure voltage difference Galvanometer: a...
  40. L

    Question：What is the difference between flux and current?

    Guys,I need to calculate the flux and current of neutron by MCNP.So what's the difference between them ,and How to calculate them? Any ideas?
  41. M

    MHB Maximising the difference between multiple distributions

    I am trying to come up with a parent loss function for the following neural network model. On top of that the algorithm for processing an image would also be helpful. The quad-tree compression algorithm divides an image into ever increasingly small segments (squares) and stops in a particular...
  42. S

    B Difference Between Redshifts of Massive Galaxies & Accelerating Galaxies

    How can someone tell the difference between a super massive galaxy's redshift and a galaxy that is accelerating away?
  43. J

    Understanding Vapour Pressure & Temperature Difference

    I have a problem at the very beginning. I don't know how to relate this vapour pressure to the temperature difference. I have read the hint: Recall the idea 7: for dynamical processes, at first, a mechanical equilibrium is reached, which means the equality of pressures; the other equilibria...
  44. Frigus

    Spermiogenesis and spermatogenesis etymology difference?

    I searched for etymology of spermiogenesis and spermatogenesis and etymology of both words is given same that is sperm + genesis. Can you please tell difference between these etymology as their is very less information given on internet about this. Thanks
  45. A

    Difference between centrifugal force vs reactive centrifugal force?

    Difference between centrifugal force vs reactive centrifugal force? and practic example
  46. Y

    Electric potential:Potential difference of test charge

    Electric potential energy at initial: Ee=kq1q2/r =(9 ×10 ^9×1.5×10^-6×(-5)×10^-6)/0.1 =-0.675J Electric potential energy at the closer point: Ee=kq1q2/r =(9 ×10^9×1.5×10^-6×(-5)×10^-6)/0.05 =-1.35J Δv=ΔEe/q =(-1.35+0.675)/1.5×10^-6 =4.5×10^5V or: Initial position...
  47. Lynch101

    I Understanding the Fundamental Difference in Interpretations of QM

    I was originally going to start a thread on individual interpretations of quantum mechanics to try to understand them better, but after reading this article by @PeterDonis it might make more sense to use that as a starting point and try to understand how the different interpretations fit into...
  48. M

    Engineering Z-transform of this Logistic Difference Equation

    Hi, I am trying to work out how I could obtain an expression for a z-transform for the following expression: x_{n + 1} = r x_{n} \left( 1 - x_{n} \right) I am hoping to derive X(z) and then use the final value theorem to show agreement with numerically calculated steady state values. I...
  49. Kaushik

    Understanding EMF and Potential Difference in Electrical Circuits

    Is emf the work done to move a positive charge from LOWER potential to HIGHER potential to maintain the potential difference or else the charges move from higher potential to lower potential and will reach a point where the potential is the same between the two points and the charge will stop...
  50. G

    I Average Number of Coin Flips to Reach a certain Head-Tail Difference?

    Let's say you keep flipping a coin until the number of heads exceeds the number of tails by 6, or vice-versa. It is very important to consider the "vice-versa". I did some digital simulations and found that the average number of flips required is about 35.4. How can we derive this number using...
Back
Top