What is Difference equation: Definition and 97 Discussions

In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given; each further term of the sequence or array is defined as a function of the preceding terms.
The term difference equation sometimes (and for the purposes of this article) refers to a specific type of recurrence relation. However, "difference equation" is frequently used to refer to any recurrence relation.

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  1. X

    Solution to nonhomogenous difference equation?

    Homework Statement Though not a single thing has been mentioned about difference equations in my signals & systems course/any courses I have taken, difference equations have appeared on the homework. It is: yn+1 + (1/5)yn = 10-n, y0 = 1 Homework Equations yp = Akn The Attempt at a...
  2. A

    A nonlinear difference equation

    Consider the equation \frac{a_n-a_{n-1}}{1+a_na_{n-1}}=\frac{1}{2n^2} I know one special solution is a_n=\frac{n}{n+1} But how to solve and find the general solution? Thanks in advance.
  3. S

    Nonhomogeneous difference equation question

    Homework Statement Find the general solution Homework Equations x(t+2)-3x(t+1)+2x(t)=3*5^t+sin(0.5πt) The Attempt at a Solution I start out by solving the homogeneous equation and end up with the two roots 1 and 2. Then I try to use the method of undetermined coefficients to find a...
  4. P

    MHB Can You Solve This Non-Constant Coefficient Difference Equation?

    I wish to solve a non constant coefficents difference equation $(x+1)y_{x+1}-(r+x)y_{x}+ry_{x-1}=0$ where r is a constant. Is there a characteristic equation and generic solution for this ?
  5. S

    Which difference equation better describes the problem ?

    http://dl.dropbox.com/u/33103477/Nicotine.png N_{t+1} = N_t - \frac{1.02}{100}N_t + 0.02 OR N_{t+1} = N_t - \frac{1}{100}N_t + 0.02 The first equation considers counts the amount the body absorbs everyday to include the amount ingested that day, the other doesn't. The answers are...
  6. S

    Difference equation modelling (check my work )

    A certain smoker has a daily intake of 0.02 milligrams of nicotine. It is assumed that 1% of nicotine is disintegrated by the body per day. (i) Set up a diference equation for the amount of nicotine N_t after t days, starting with an initial level of N_0 = 0. (ii) Derive a closed form...
  7. P

    LTI Difference Equation from Impulse response

    I've been told that to calculate the difference equation of an LTI system, you simply take the sample values of the impulse response as the coefficients of the x[n-k] terms in the difference equation. i.e. if h[n] = {1, 0.5, 0.25, 0.125} for n>=0, then y[n] = x[n]...
  8. chisigma

    MHB Difference equation tutorial: draft of part II

    Dear friends of MHB in this thread some aspects of the difference equation of degree greater than one are investigated. For size limitation the tutorial is divided into several sections. As for the part I, suggestions, observations, requests of clarification and improvements are welcome...
  9. C

    Science and engineering math: Difference equation, non-homogeneous

    Homework Statement Solve the difference equation: an+2 - 5an+1 + 6an = 4n Subject to a0 = 0 & a1 = 1 Homework Equations an = Arn The Attempt at a Solution I got two solutions for the first part for when it is homogeneous by substituting an = Arn into the equation and solving for...
  10. chisigma

    MHB Difference equation tutorial: draft of part I

    Dear friends of MHB some months ago I wrote for MHF a tutorial on the Difference equations and the reason of that was the difficulties I noticed in the treatment of difference equations, an important chapter of Discrete Maths that [may be...] is a little unfairly undervaluated. Request by the...
  11. T

    Difference equation, ypn guess problem

    Homework Statement Solve the difference equation Homework Equations y[n+2]-3y[n+1]+2y[n]==4n*2^n, n>=0 y0=0,y1=1 The Attempt at a Solution 1. Homogenous solution: Characteristic equation => r^2-3r+2==0 <=> r1=1,r2=2 => yhn = C1*1^n+C2*2^n 2. Particular solution: ypn = ? I...
  12. S

    From a transfer function to a difference equation

    Hello. I have been given a transfer function for a digital system, and I need to find the difference equation for that system. I have attached a pdf with my work. I would be grateful if someone could take a look at it, and see if I am along the right lines. Thanks in advance, and happy...
  13. T

    Solve first order difference equation

    Homework Statement Solve the first order difference equation. Homework Equations x[n] - x[n-1] = n(n+1)/2 x[1] = 1 The Attempt at a Solution Homogenous solution: Characteristic equation: r - 1 = 0 <=> r = 1 => yhn = C * 1^n = C Particular solution: ypn = ? I'm supposed to...
  14. C

    Analysis of two variable Non-linear difference equation

    Hey everyone, My understanding of difference equation is very limited and, after consulting a few books, I decided to post this here to get some ideas or at least some references on where to look. I have a symmetric first order difference equation system in two variables, X and Y. Though...
  15. L

    Difference Equation and Dirac Delta

    Homework Statement y[n] - (2/3)y[n-1] = x[n] what is y[n] if x[n] = diracdelta[n] The Attempt at a Solution for some reason, i argued that y[n-1] = diracdelta[n-1] so y[n] = diracdelta[n] + (2/3)diracdelta[n-1] Im pretty sure this is wrong, anybody can help?
  16. J

    Find the particular solution of this difference equation (solve most of it)

    Homework Statement Find the particular solution. y(k+2) + y(k+1) -6y(k) = 3^(k) Homework Equations The Attempt at a Solution Still need to be answered Question (1): Before finding the particular solution, is it true that we should ALWAYS get the homogeneous solution...
  17. J

    Problem with substitution in a difference equation

    Homework Statement Verify that the response of the system governed by the 1st order different equation y(k)=bu(k)+ay(k-1) is given by this solution y(k)=\frac{b}{1+a}\left [ (-1)^{k}+a^{k+1} \right ] for u(k) = (-1)^k The Attempt at a Solution The solution said we can verify this...
  18. F

    Linear difference equation with vanishing inhomogeneity

    Hi, I am new to this forum and apologize for bothering you with my question on recurrence/difference equations. Unfortunately I was unable to find an answer in textbooks etc., so I would really appreciate a short answer or a reference to relevant literature. The problem is as follows: Say...
  19. H

    How do we add the affect of the sampling rate to the difference equation?

    I designed four different transfer function to differentiate and accumulate a given function. In my example, the given function is sin() between [0, 6*PI]. Dashed blue line: The original input function (i.e.; sin(t)) Red line: Integration of sin(t) with initial value of -1.0. (H(s) = 1/s)...
  20. R

    Solve for A_n as n→∞: Difference Equation

    This is a bit of a shot in the dark, but has anybody ever encountered a theory which can tell me what the solution of this equation: A_n = nA_{n-2} + nA_{n-3} behaves like, as n\to\infty? For convenience, you can set A_n = 1 for n = 0, \ldots, 3. Without the term on the right, it goes...
  21. I

    Looking for General solution for a difference equation

    At+1=(At+r)/(At+r+1) A1=constant I know I can set At+1=At=A and solve for a special solution. What would be a general solution? I am not taking a course in Difference Equation, and this is not my homework but I encounter a similar question and I reduce it to this form. Thanks
  22. S

    System of nonhomogeneous difference equation

    How do you solve the system z(t+1)=Az(t)+b where A is a 2x2 matrix and z(t+1), z(t), b are 2x1 matricies? I solved the homogeneous solution: z(t)=P(D^t)(P^-1)z(0) where D is the diagonal matrix of eigenvalues of A and P is the matrix of eigenvectors. I tried to solve the nonhomogeneous...
  23. J

    Solve Difference Equation: Find β for x_k=x_{k-1}+x_{k-2}

    Homework Statement In analogy with differential equations, the difference equation x_{k}=x_{k-1}+x_{k-2} has two solutions x_{k}=\beta^{k} for some \beta\neq0. Determine the two possible values of \beta. Homework Equations x_{k}=x_{k-1}+x_{k-2} x_{k}=\beta^{k} \beta\neq0 The...
  24. S

    Difference equation vs differential equation

    Hi, Im trying to go back and relearn material from a signals class I took to prepare for my controls class. In the controls class we always deal with CT systems, whereas in the systems class we focused on DT. My prof derived a frequency response that was H(w) = 1/(1-a*exp(i*w)). This...
  25. L

    Finding the difference equation given the impluse response

    This question is for a DSP class. I hope that I am posting somewhere appropriate. So given the impulse response: h[n]=((0.5)^n-(0.25)^n)u[n] find y[n]. Where do I start? I don't need an answer, just a nudge in the right direction.
  26. B

    Difference equation with non-linear term

    Hi all-- I can't figure out how to approach the following difference equation: ax_{t}+f(x_{t-1})+bx_{t-2}=e_{t} where a, b are constants, e_t is a known function and f(x_t-1) is a convex, u-shaped function that goes through the origin. (Sorry Tex would not want to work) To begin with, I...
  27. R

    MATLAB Finding q501 for Difference Equation: Solving with Matlab

    I want to find q501 for the difference equation: qn=qn-1 - 0.001 q2n-2 n≥2, q0=1, q1=2 I thought it's easier to do this on Matlab & I tried to write a script file for this problem: k=0.001 q(1)=1 q(2)=2 for n=1:502 q_n=q_n-1-k*(q_n-2)^2 end I don't know why my code...
  28. phoenixthoth

    How Can a Closed Form for This Complex Difference Equation Be Determined?

    While working on another problem, the following difference equation came up. s_{n}=\frac{1}{r_{1}-r_{1}^{n}}}\sum_{k=1}^{n-1}s_{k}B_{n,k}\left( r_{1},r_{2},...,r_{n-k+1}\right) The B_{n,k} are (nonlinear) polynomials in the variables r_{1}, ..., r_{n,k-n+1} that don't involve the s's...
  29. H

    Solve Difference Equation | General Solution | No Particular Solution

    Homework Statement Given difference equation T(a+2)-7T(a+1) +6T(a)= 6f Find the general solution of this equation Homework Equations I have found the auxiliary equation be A(1)^n+B(6)^n But seems can't find the particular solution of that question. Is it impossible to do this...
  30. S

    Solve Difference Equation: y(n)-y(n-1)+0.25y(n-2)=x(n)-0.25x(n-1)

    Hi guys I have this difference equation. y(n)-y(n-1)+0.25y(n-2)=x(n)-0.25x(n-1) I found the step response of the system from the homogeneous solution and it's yh(n)=C1(0.5)n+C2n(0.5)n >>>homogeneous h(n)=(0.5n+1)(0.5)n >>> step response The 2nd part of the problem is I'm supposed to...
  31. G

    Converting finite difference equation to matrix equation

    http://e.imagehost.org/0218/question.jpg I think I've managed to create the finite difference equation in part a), but I'm not sure how to turn this into a matrix equation. Any advice would be appreciated!
  32. D

    Difference Equation: Explained & Derived - QM1

    In the following link: http://electron6.phys.utk.edu/QM1/modules/m2/square_potentials.htm what does the difference equation mean, and how is it gotten from the previous step?
  33. Link

    Stochastic difference equation?

    Homework Statement This is a question about one single step of a solution of a long equation. http://www.geocities.com/link_herooftime/math.jpg where P, U and V are variables. a, b, c, d are constants and t is the time, which are measured in discrete periods. The question is how...
  34. F

    Solve Difference Equation for c_n

    Homework Statement Find a closed-form expression for c_n. c_{n+1} = \frac{c_0 (3c_n + c_0)}{2c_n + c_0} Homework Equations The Attempt at a Solution Besides finding c_1, c_2, c_3, \ldots and looking for a pattern, I have absolutely no idea.
  35. W

    Difference Equation Explained by Oppenheim

    This is some math from "Discrete-Time Signal Processing" by Oppenheim: We have the homogeneous difference equation: \sum_{k=0}^N a_k y_h [n-k] = 0 "The sequence y_h[n] is in fact a member of a family of solutions of the form: y_h[n] = \sum_{m=1}^ N A_m z^n_m " So what is Oppenheim...
  36. R

    Implementing Difference Equation in MATLAB

    please help me to implement this difference equation in MATLAB? y[n]=x[n]-x[n-1]; matlab is not supportin -ve index...
  37. E

    Engineering Difference equation of simple RLC Circuit

    I have been having a difficult time understanding how to determine the input/output difference equations of a circuit. I believe I am good on series circuits but would like some feedback on Series/parallel determinations. Please look at included file and see if I am on the correct path.
  38. E

    Help with this difference equation

    Let be the equation: A(2n)-A(2n-1)=3 i,m a bit stuck..i don,t know how to solve it :frown: :frown: it it weren't for the 3 term i would try A(n)=r^n where r is an unknown number..however the 3 factor spoils all..also we could try the identity...
  39. D

    Solving Difference Equation Involving Complex Numbers

    This is not quite a homework question, but I hope close enough that it can be posted here. I'm going through a signal processing book on my free time, doing all the problems and so on, and I've come across a problem which I'm not too sure about how to solve. Here it is-- Consider the...
  40. B

    Solving First Order Difference Equations

    I am currently struggling to solve Difference equations (especially the first order ones). Here is a 'simple' one which I cannot get the correct answer to despite trying many times. Here is what I think is my most decent attempt. 2y_{n + 1} = y_n + 2 Rearranging gives y_{n + 1} =...
  41. B

    Solving Difference Equation: w_n = 2^n w_0 + 2^{n + 1}-1

    Hi, I've been working on a difference equation and I just can't get the answer. Can someone checking my working? w_{n + 1} = 2w_n + 1 w_1 = 2w_0 + 1 w_2 = 2w_1 + 1 = 2(2w_0 + 1) + 1 = 2^2w_0 + 1 + 2^1 \Rightarrow w_n = 2^n w_0 + \sum\limits_{i = 0}^{n - 1} {2^i } = 2^n w_0 +...
  42. M

    How do I set up difference equations for intersecting ovals?

    Ok, I am not sure if this is the right section, but seeing that difference equations are the discrete version... Now the question is : Into how many regions do n simple ovals divide the plane, given that every oval meets every other oval in two points and no point in the plane is common to...
  43. phoenixthoth

    A nonlinear difference equation

    I'm posting this under analysis because of the method I'm thinking about using to solve it. Here is the equation: \varepsilon \left( x\right) =e^{\varepsilon \left( x-1\right) } and the initial condition is \varepsilon \left( 0\right) =1. My main goal is to consider x as a number in...
  44. E

    MATLAB Matlab for loop and difference equation question

    I'm attempting to solve a difference equation y(k+1) = -0.5*y(k) + x(k) where y(0) = 0 and x(k) is in my case a unit step function ie = 1 well, I'm trying to solve this using a for loop, but am having some trouble. The code I've generated gets an error, "Index into matrix is negative or...
  45. A

    Simplify in sum and difference equation

    I was never taught how to do this I was just given problems with no solutions so I don't know what to do can someone please help me I have two questions which are similar maybe if I get help with one I can solve the other one on my own. It says simplify the following \cos(\pi+x) + \cos...
  46. phoenixthoth

    What's the solution to this difference equation?

    an+1=2an where n is a natural number and a0 is some fixed real number. (in case it's not clear, what's on the right hand side is 2 to the an power.) thanks! i'm wondering if it will be possible to let n=1/2 and have the half iterate to 2^x i was looking for earlier, where by that i mean a...
  47. J

    How Do You Calculate Phase Difference and Minimize Sound Between Two Speakers?

    Hi i posted here before and got great help, and I ran into another problem maybe you can help me this is the question. Two loud speakers are placed on a wall 2.00 m apart. A listener stands 3.00m from the wall direclty infront of one of the speakers. A single ocillator is driving the speakers...
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