Questions tagged [difference-equations]

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

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3
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1answer
98 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 ...
6
votes
3answers
317 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 ...
0
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1answer
37 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 ...
3
votes
1answer
77 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 ...
0
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1answer
39 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 ...
2
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2answers
149 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[0] == x^10}, g, {n, 0, 5}] This code ...
1
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2answers
87 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.
3
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1answer
66 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
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1answer
52 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
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1answer
145 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
2answers
97 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 ...
0
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1answer
31 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. ...
0
votes
1answer
79 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: ...
2
votes
1answer
69 views

Solving recurrent equations with RSolve

I am trying to find a[0] by solving the following system of equations where n can get 1,2,3,...,m-1 ...
1
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0answers
44 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
1answer
73 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
1answer
99 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} ...
0
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1answer
40 views

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. ...
0
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1answer
61 views

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 ...
2
votes
3answers
274 views

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]+...
1
vote
1answer
34 views

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: ...
3
votes
0answers
61 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 ...
3
votes
1answer
178 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? ...
4
votes
2answers
393 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 $a$, $b$...
1
vote
1answer
72 views

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 ...
1
vote
2answers
266 views

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)=\...
0
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0answers
46 views

Difference Equation system

I am new in Mathematica and I have a very large system of difference equations like: ...
5
votes
3answers
187 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] ...
4
votes
2answers
135 views

How can I solve a functional equation with domain restrictions?

I have three properties for a function: ...
0
votes
1answer
52 views

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_{...
2
votes
1answer
136 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 ...
0
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0answers
72 views

Trying to implement an algorithm to solve a self-consistent Bloch-Schrodinger Equation

I am trying to understand and to implement an algorithm described by Kunimi-Kato in their supplementary material to solve the self-consistent equation below $$ \left[\frac{\hbar^{2}}{2m}|\boldsymbol{G}...
0
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1answer
209 views

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 ...
4
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2answers
200 views

eigenvalue and eigenfunction of complex euler-bernoulli beam

So I am new to Mathematica and am trying to solve the euler-bernoulli modal equation for a U-shaped Cantilever beam given by equations :- where i is the index of the region. In total there are 2 ...
0
votes
0answers
41 views

Parametrization of twisted pseudospheres types 2 and 3

Among the three types of rotationally symmetric Pseudospherical surfaces $K=-1$ (Beltrami central, type 2 and type 3) (http://xahlee.info/surface/gallery.html) we have Dini twist addition term $ b\...
2
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3answers
171 views

Nonlinear Difference Equations [closed]

How can I plot the nonlinear difference equations?
0
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1answer
35 views

Why does DifferenceRoot evaluate only in this table?

I would like to use a complicated function containing DifferenceRoot as a replacement rule, but somehow it evaluates only in ...
0
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0answers
31 views

Solve ODE transformed into q-difference in Mathematica

Let's take a simple differential equation: $\frac{dx}{dt} = -x(t)$ Suppose we want to do a q-transform. To do this, we will replace the time derivative $\frac{d}{dt}$ with the q-derivative (also known ...
0
votes
1answer
94 views

How I can plot the below map?

I have tried to plot the following map: $\qquad \begin{cases} y_{n+1}=r y_n^{x_{n+1}-x_{n+2}}\\ y_1=x_1-x_2 \quad \end{cases}$ using the code shown below. The error I have got is that x[1] - x[2] ...
1
vote
1answer
62 views

A modular version of LinearRecurrence?

I'm playing around with implementing the Lucas probable prime test (mainly so I can understand it better), and would love a version of the LinearRecurrence function that used addition modulo n (with n ...
0
votes
2answers
109 views

Plot linear difference equations

How can I plot an unstable node, saddle, and center in linear two-dimensional difference equations? I can plot the stable node, please see the code. Thank you in advance. ...
1
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0answers
41 views

Solving a difference equation involving summation expressions-Implicit output

I am trying to solve a difference equation involving summation expression with the following code: ...
1
vote
0answers
47 views

How to study convergence of recurrence relations?

Is there a way to test the convergence of a recurrence relation in Mathematica? For example does this relation converge: $$a_{n+1}=a_n \dfrac{n-\dfrac{1}{4}+c^2}{-5+5c^2}$$ for some values of the ...
1
vote
1answer
108 views

How to solve this recurrence equation with Mathematica?

I am interested in solving this recurrence relation (equation) with Mathematica code. I am new to Mathematica. I tried RSolve, RSolveValue, AsymptoticRSolveValue commands for this. But I am not ...
3
votes
3answers
381 views

Problem plotting a bifurcation diagram of logistic map

I would like to plot a bifurcation diagram from the logistic map (difference equation) of the type $$ x_{t+1} = r\,(1-x_{t})\,x_{t}. $$ The code I used for that was ...
0
votes
1answer
67 views

Making change of variable

I have the following expression $$L=\frac{m}{2}\left(\dot{q}^{2} \sin ^{2} A t+\dot{q} q A \sin (2A t)+q^{2} A^{2}\right)$$ with $q=q(t)$ I want to make a change of variabl $$Q=q\sin(At)$$ By hand I ...
3
votes
1answer
155 views

Solve 2D Difference Equations

If I have a system of difference equations $$ \begin{cases} x(n + 1) = x(n) + x(n) y(n) + y(n)^2 \\ y(n + 1) = y(n) - x(n)^2 + y(n)^2 \end{cases}, \text{ with } \begin{cases} x(0) = 1\\ y(0) = 2 \end{...
2
votes
1answer
162 views

Plot system difference equations

Is this way correct to plot system of difference equation. For example ...
2
votes
1answer
147 views

Phase portrait for three dimensional system of nonlinear difference equation using Mathematica

I am a student of M.Phil Mathematics. I am working on a non linear system of difference equations in three dimensions. I want to draw a phase portrait for my system using Mathematica. I was trying ...

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