# Questions tagged [difference-equations]

Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.

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### Solution of a recurrence relation

I want to solve $a_{n+1} = (1 + \alpha) a_n + \gamma$, where $\alpha$ and $\gamma$ are some constants. Wolfram alpha returns: $a_n = \frac{\gamma ((1+\alpha)^n-1)}{\alpha} + c (1+\alpha)^{n-1}$. Any ... 1 vote
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### Recurrence relation for B-spline polynomials

I am trying to get the explicit polynomials of cardinal B-splines. So far I have this implementation (for cardial B-splines of degree 3 on the knots 0, 1, 2, 3): ...
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### RSolve with integer and boolean variable

I have a recurrence relation with two variables $i, b$ where $i \in \{0, \ldots, n-1\}$ for some parameter $n \in \mathbb{N}$; and $b\in \{0,1\}$. I tried to solve it using RSolve, but the function ...
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In short, I want to solve a recurrence equation in two variables with multiple boundary conditions. In more detail: For instance, suppose I want to compute $a[0,j]= 1 \quad \forall j$ $a[i,0]= 1 \quad ... • 251 2 votes 2 answers 164 views ### RSolve with two boundary conditions I want to solve a recurrence equation that has boundary conditions on both sides:$a= 1a[n]= 10a[i] = a[i-1]-a[i+1]\quad \forall i \in \{1, \ldots, n-1\}$This should be a well defined ... • 251 3 votes 2 answers 60 views ### Need help formatting DifferenceRoot for LaTeX I want to put this into LaTeX format. What do I do? (FindSequenceFunction[Join[{5, 3, 3, 2}, Table[2, {80}]], k + 1] + n - 1) -1 + n + DifferenceRoot[Function[{[FormalY], [FormalN]}, {16 - 8 [... • 2,298 1 vote 1 answer 185 views ### How to plot the "trapping region" in Henon Map? I am writing a paper that makes use of the Henon map. I have managed to plot the Henon map but now require plotting the "trapping region" shown in the image. Do I require to plot it as a ... 2 votes 2 answers 86 views ### Inverse of an Animation I was thinking, it's possible to plot inverse an animation?? ... • 391 3 votes 1 answer 79 views ### Difference between NDSolve and RecurrenceTable I have the following system which I model as difference equations and solve with RecurrenceTable: ... • 2,723 3 votes 1 answer 75 views ### Replace previous equations into the current one in a recurrence relation I have a recurrence relation given as follows: f[k + 1] == 1/a[k, k + 1] Sum[a[k, k - k1] f[k - k1], {k1,0,k-1}] Evaluating it for ... 2 votes 1 answer 106 views ### How to reproduce Asymptotic Bounds of Recurrences in Wolframalpha In Wolframalpha's Examples for Recurrences, there are bunch of Asymptotic Bounds of Recurrences examples, like this It can get perfect result: ... • 213 1 vote 1 answer 102 views ### RSolve unable to solve the equation I gave the following code as input: RSolve[x[n + 1] == 1/2 x[n] + 2 Log[x[n]], x[n], n] Mathematica gave the same output: ... 0 votes 0 answers 49 views ### Equal equations or Expressions I would like to check if equation (Sigmaa22) is the same as equation (stress) Basically i have 2 equations one is called Sigmaa 22 and the other one is called stress,My problem when i try to check if ... • 37 0 votes 1 answer 107 views ### Recurrence Table for a specific Recurrence I wanted to know how can one find an arbitrary number of terms of the non-linear recurrence (using software, like maple)such as $$a_{2n-1}=-\sum_{j=1}^{n}{n+j-1\choose 2j-2}a_{n+j-2}, \ a_{0}=-1$$ $$... 0 votes 1 answer 112 views ### Mathematica stuck on partial derivative calculation I was experimenting polynomial gradient descent on Mathematica, but it got stuck on partial derivative calculation. Formula below: Traditional Form:$$ mse = \frac{\sum_{i=1}^{n}\left(y[[i]] - \left(a\... • 139 3 votes 2 answers 210 views ### Numerical solution of the 2D-spatial nonlinear Allen equation I would like to solve the 2D-spatial Allen equation in rectangular coordinate, which is a nonlinear reaction-diffusion PDE of the type $$\partial_{t}u=\epsilon(\partial_{xx}+\partial_{yy})u + u - u^{3}... • 1,120 0 votes 0 answers 96 views ### How to Solve this recurrence relation? When I use RSolve[] [![enter image description here]] It would show this. I want to solve it to a[n], the function of n & E How to do that? The original ... • 23 0 votes 0 answers 44 views ### Introducing FindRoot in a ReccurrenceTable but problem with the starting point I would like to introducing FindRoot in a RecurrenceTable, that uses the previous result as a starting point. My equations are defined as following: ... • 1,235 0 votes 0 answers 87 views ### Different solutions for an equation I have a problem with Mathematica, When I solve this equation in Mathematica and also in wolframalpha I have different solutions [ ... • 105 2 votes 1 answer 94 views ### How do I make a second order differential equation match a difference equation? I have fitted a difference equation to some data and would now like to find a differential equation that matches the difference equation. The difference equation and differential equation are$$ y(n)=... • 14.8k 3 votes 1 answer 127 views ### How to use Manipulate with ListLinePlot I'd like to run Manipulate with 0<r<=4 that preserves the ListLinePlot of the recurrence table given with the colors shown. I'm looking to use the autorun feature in Manipulate to show how the ... • 1,103 6 votes 3 answers 419 views ### How to Generate a Phase Portrait for a Jacobian Evaluated at Fixed Points Consider the following: The Jacobian matrix J given below correctly generates the eigenvalues for the (x,y) fixed point shown below. When looking at the stability of the fixed point the absolute ... • 1,103 0 votes 1 answer 48 views ### Substitution of sequences to derive recursive mean I would have the following derivation to calculate the recursive moving average and I'd like to follow it as closely as possible in Mathematica. For the sequence where$y(i)$is considered as an ... • 373 3 votes 1 answer 95 views ### Implementing solution of a system of recurrence relations [closed] Let us consider a system of recurrence relations such as$ a_{n-1} = ( \lambda_1 + n \lambda_2 ) a_n + \lambda_3 b_n  b_{n-1} = ( \lambda_4 + n \lambda_2 ) b_n + \lambda_5 a_n $subject to the ... • 33 0 votes 1 answer 44 views ### RecurrenceTable for computing Required Minimum Distributions from an IRA Here is a list of required minimum distributions from an IRA based on IRS published life expectancy tables for a particular age ... • 649 2 votes 2 answers 170 views ### RecurrenceTable does not work for sequence of function Consider the following code that repeatedly differentiates a function: test = RecurrenceTable[ {g[n] == D[g[n - 1], x], g == x^10}, g, {n, 0, 5}] This code ... • 933 1 vote 2 answers 92 views ### Im trying to write this in Mathematica. It is a recurrence relation for convolution [duplicate] I have tried many things, the relation is in the following picture, x' is a dummy variable. • 11 3 votes 1 answer 89 views ### RSolve solves only one of two equivalent recurrences I am having an issue with the RSolveValue/RSolve function. Specifically, Mathematica is able to correctly evaluate ... 0 votes 1 answer 62 views ### How can I calculate the differentiation of qi in mathematica if I have the sum in the equation? How can I calculate the partial differentiation of qi in the next equation? -1 votes 1 answer 155 views ### Please I need help, how can I solve this heat impulsive system? [closed] Please I need your help!! I need to solve the following system: $$\left\{\begin{array}{ll} \partial_{t} \psi(x,t)-\Delta \psi(x,t)=0, & (x,t)\in (0,1) \times((0, 2) \backslash\{1\}) \\ ... 2 votes 2 answers 126 views ### Computing periodic points of some function Given a function h[{x_, y_}, b_, c_] := {x^2 + c - b*y, x} for some parameter values b and c ... • 713 0 votes 1 answer 38 views ### RSolve problem not working I tried to use Mathematica to find a_{n}. But unfortunately, it returned a equation that I can't understand. Here is the code below. ... • 1,611 0 votes 1 answer 81 views ### Removing hypergeometric solutions in RSolve [closed] I am using RSolve to find solutions, but I am only interested in rational solutions. For example here: And here is the input code: ... 4 votes 1 answer 175 views ### Solving recurrent equations with RSolve I need to find (or guess?) the symbolic functional form of aFun[n] for a general n (where n>=1). Anyone can help? ... 1 vote 0 answers 55 views ### Defining general recurrence expression and extracting coefficient I'm new to Mathematica and I wish to solve a difference equation which is defined by the relation: y_{i-1}-2y_{i} +y_{i+1} = f(x_i,y_i),\\y_0 = a, y_n = b.. Where x_i is given for all i. I want ... 1 vote 1 answer 137 views ### Finding fixed points of a system of difference equations Can anyone help me in finding the fixed points of the systems satisfying all the parameters are real, positive?$$x_{n+1}=x_{n-d}e^{(r(1-\frac{x_{n-d}}{k})-\frac{\beta y_{n-d}}{(x_{n-d}+\gamma)}+x_{n-... 4 votes 1 answer 115 views ### How to solve for multiple (cascading) recurrence relations I am working with recurrence relations with a simple base: \begin{equation} Y_i = aY_{i-1} + (1-a)X_i \quad \mbox{and if$Y_0=0\$ then} \quad Y_n = (1-a)\sum_{i=1}^n a^{i-1} X_i \tag{1} \end{equation} ...
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Input: Sum[HarmonicNumber[k]/k^2, {k, 1, m}] That is $$\sum_{k = 1}^{m} \frac{H_k}{k^2}$$ Output I will attach a screenshot for I don't even know how to write ...