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
161 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
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2answers
279 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
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1answer
65 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 ...
0
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2answers
121 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
39 views

Difference Equation system

I am new in Mathematica and I have a very large system of difference equations like: ...
5
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3answers
160 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
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2answers
112 views

How can I solve a functional equation with domain restrictions?

I have three properties for a function: ...
0
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1answer
38 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
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1answer
126 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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0answers
39 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
144 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
161 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
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0answers
35 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
137 views

Nonlinear Difference Equations [closed]

How can I plot the nonlinear difference equations?
0
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1answer
30 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
30 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
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1answer
91 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
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1answer
55 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
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2answers
90 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
37 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: ...
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0answers
38 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
81 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
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3answers
259 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
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1answer
55 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
128 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
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1answer
83 views

Plot system difference equations

Is this way correct to plot system of difference equation. For example ...
2
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1answer
107 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 ...
4
votes
2answers
124 views

Using RSolve for recurrence equation

I'd like to use Mathematica to verify the solution to a recurrence equation. I have the following equation: $Q_{k+1} = Q_k + \alpha(r_{k+1} - Q_k)$. I also have a derivation showing how to obtain a ...
1
vote
1answer
62 views

difference equation and continued fractions

I'm interested in solving the following difference equation: $x[k-1]+(k^2+k+a)/x[k]=b$, $k=1,2,\ldots$, where $a,b$ are fixed positive numbers; let's say $x[1]=c>0$. Mathematica's ...
2
votes
2answers
139 views

Counting the number of binary strings of length m with no consecutive 1s (RR). How to improve it?

I am new to Mathematica and I am trying to solve this problem of counting the number of binary strings of a certain length m, as far as no consecutive 1s are there. For instance m = 3, my recurrence ...
0
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1answer
75 views

How to plot the roots of two complex equations?

I have these two equations as two variables '$a1$' and '$b1$', mentioned below and I want to plot the roots of $a1^{\dagger}*a1$ with respect to P0, which will give me bistable plot with three values. ...
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0answers
38 views

General question about RSolveValue and general programming

If I have the following code: ...
1
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0answers
79 views

Plot a stable 4-periodic orbit

I have a question guys In Mathematica how I can plot a stable 4-periodic orbit in the logistic map with giving the four x values for the orbit and find the a value for which it goes through a period ...
3
votes
1answer
41 views

How to use elements of tables in recurrence tables?

I am trying to use a List inside a RecurrenceTable. Suppose I have the list ...
0
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2answers
74 views

Trying to generate strings using Recurrence Table

I'm trying to generate strings recursively that look like this: ...
1
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0answers
70 views

Dirac Operator in de Sitter background

I am attempting to write the Dirac operator in a curved background, and eventually solve the equation as a second order PDE, since I am attempting to bring it into Klein-Gordon form. Essentially what ...
0
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1answer
55 views

Problem in table [duplicate]

NDSolve[{t,Evaluate[{ode}\.Sol]},{t,0,10,1}]//TableForm After executing this with appropriate equations I get solution in the tabular form but when I try to ...
4
votes
2answers
318 views

How to plot a system of recurrence equations

I have the following code working well ... but I would then like to plot M[k] and L[k] on the same axes with k along the horizontal and M[k] and L[k] values along the vertical. The graph I'm looking ...
2
votes
1answer
82 views

How do I create a bifurcation diagram for the below iterative map? [closed]

I have tried to create a bifurcation diagram for the following iterative map: x[n+1]=-r Log x[n], x[1]=0.711 and r=1/log(n(n+1)) using the following code But it doesn't work. Any help? ...
2
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1answer
50 views

Using NIntegrate inside RecurrenceTable

I'm trying to solve self-consistent equations of the form ...
0
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1answer
97 views

Plot 2-D system difference equations

If I have 2-D system difference equations x(n+1)=x(n)-5y(n) , y(n+1)= 2x(n)+y(n) I need to plot this system. I did : ...
1
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0answers
56 views

plot discrete system by mathematica

if I have a discrete system x(n+1)= 0+y , y(n+1)= -0.5x +0 The fixed point (0,0) is center by Jacobian., I do not know how Plot this by using Mathematica code to get center. I am thankful if any one ...
1
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0answers
36 views

How to apply RecurrenceTable or Array in two dimensions

This question relates to 104959. How can I solve the following (akward) code by using RecurrenceTable or Array? ...
3
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0answers
72 views

Compute the sum given a recursion for each summand

I have a system of two recursive equations with two unknowns A[n] and B[n] which apparently Mathematica can't solve RSolve not ...
0
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0answers
51 views

Nest function n times

A trivial example would be f[x_]:=x Nest[f, 7, n] which would of course be 7 because it is independent of ...
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0answers
40 views

RSolve not evaluating when given my system of recurrence equations

I am trying to solve the following system of recurrences with RSolve: ...
3
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4answers
95 views

RecurrenceTable for systems of linear difference equations

I'm working on a project that involves developing a financial forecasting model. The equations used in the model will largely be linear difference equations (estimated via some form of regression ...
2
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0answers
37 views

RecurrenceTable doesn't evaluate with constant right-hand side

One of my functions automatically generates systems for RecurrenceTable. Usually works fine, but today I encountered a problem. If the right-hand side is a ...
0
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0answers
217 views

Help with “Coordinate should be a pair of numbers, or a Scaled or Offset form.”

I am plotting the pair of recurrence relations: ...

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