Questions tagged [difference-equations]

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

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RSolve two variables with multiple boundary conditions

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 ...
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RSolve with two boundary conditions

I want to solve a recurrence equation that has boundary conditions on both sides: $a[0]= 1$ $a[n]= 10$ $a[i] = a[i-1]-a[i+1]\quad \forall i \in \{1, \ldots, n-1\}$ This should be a well defined ...
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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 [...
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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 ...
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2 votes
2 answers
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Inverse of an Animation

I was thinking, it's possible to plot inverse an animation?? ...
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3 votes
1 answer
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Difference between NDSolve and RecurrenceTable

I have the following system which I model as difference equations and solve with RecurrenceTable: ...
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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 ...
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1 answer
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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: ...
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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: ...
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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 ...
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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 $$a_{2n-1}=-\sum_{j=1}^{n}{n+j-1\choose 2j-2}a_{n+j-2}, \ a_{0}=-1$$ $$...
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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\...
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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}...
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How to Solve this recurrence relation?

When I use RSolve[] [![enter image description here][1]][1] It would show this. I want to solve it to a[n], the function of n & E How to do that? The original ...
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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: ...
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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 [[1] ...
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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)=...
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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 ...
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6 votes
3 answers
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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 ...
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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 ...
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3 votes
1 answer
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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 ...
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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 ...
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2 answers
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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[0] == x^10}, g, {n, 0, 5}] This code ...
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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.
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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 ...
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1 answer
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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?
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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\}) \\ ...
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2 votes
2 answers
114 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 ...
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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. ...
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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: ...
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4 votes
1 answer
172 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? ...
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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 ...
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1 answer
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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-...
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4 votes
1 answer
112 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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1 vote
1 answer
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How we write Recurrence functions and Generate individual components using given condition

How we write the recurrence function of below code so that it can easily find remaining components such as U[3], U[4], etc. ...
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1 answer
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Understanding a "strange" output about a finite sum

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 ...
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3 votes
3 answers
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How to draw discrete dynamic systems in mathematica

How to find invariant sets in nonlinear discrete dynamical systems. How to draw discrete dynamic systems in mathematica? $$x[n+1]=f(x[n],y[n]), y[n+1]=g(x[n],y[n])$$ example $$x[n+1]=0.9*y^2[n]/(y[n]+...
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1 vote
1 answer
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How to print out exclusively even terms of a sequence?

I need to print out the first 20 even-numbered terms of the function $a_{n+1}=\frac{5}{a_n}$. I am capable of printing out each term with this code: ...
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3 votes
0 answers
64 views

Closed form solution for a differential-difference equation

Considering a differential - difference equation : $$g (t + 1,s) = \cosh (s) + \frac {\alpha} {t}\sinh (s)\frac {d} {ds} g (t,s)$$ with $g (t, s = 0) =1$, I am looking for a closed form for its ...
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1 answer
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Boundary condition do not satisfied

...
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3 votes
1 answer
193 views

Using dynamic programming to compute an integer sequence

Let a[n] = n + 1 - a[EulerPhi[n]], n integer > 0. I have Python code that generates the sequence using dynamic programming. How can I achieve the same thing elegantly/idiomatically in Mathematica? ...
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4 votes
2 answers
479 views

Plotting an image of a discrete dynamical system

I am trying to plot a discrete dynamical system of the form $$\vec{x}_{k+1} = A \vec{x}_k$$ where $A$ is a $2\times 2$ matrix in the form $$\begin{pmatrix}a&b\\c&d\end{pmatrix}$$ where $a$, $b$...
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1 vote
1 answer
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problem in solving a non linear differential equation

I'm trying to reslove a differential equation with one of the coefficents depending on the dependent variable, it's a simple dynamic system, with one of the coefficients that can assume 2 values: The ...
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1 vote
2 answers
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Chebyshev polynomials

How could I write the Chebyshev polynomial as a function that uses Nest? Also, how could I write it using recursion? Furthermore, how can I show that $T_n(x)=\...
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Difference Equation system

I am new in Mathematica and I have a very large system of difference equations like: ...
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5 votes
3 answers
240 views

2 issues with ListDensityPlot

I am using Mathematica Version Number 12.0.0.0 Platform: Microsoft Windows (64-bit) The FIRST issue is that the ListDensityPlot is not plotting values of x[Tfinal] ...
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4 votes
2 answers
148 views

How can I solve a functional equation with domain restrictions?

I have three properties for a function: ...
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1 answer
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Simulation of a recursive stochastic process

I would like to simulate and plot multiple paths of the following stochastic difference equation, for any initial condition $\pi_{0} \in (0,1)$: $\pi_{t+1} = \gamma \pi_{t}$ with probability $1/3 \pi_{...
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2 votes
1 answer
137 views

Could anyone help me to compute the following code?

The following code works good when the value of " r < 21 ". But when r > 20, I get the following error message ...
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1 answer
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Bifurcation diagram for coupled nonlinear difference equations

I’ve been trying to plot bifurcation diagram of 2D map following the example by Chris K in here, where I managed to plot few of periodic cycles EDIT ...
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