Questions tagged [difference-equations]
Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.
258
questions
0
votes
0answers
45 views
3
votes
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
votes
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
vote
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
votes
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
votes
0answers
39 views
Difference Equation system
I am new in Mathematica and I have a very large system of difference equations like:
...
5
votes
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
votes
2answers
112 views
How can I solve a functional equation with domain restrictions?
I have three properties for a function:
...
0
votes
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
votes
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
...
0
votes
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
votes
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
votes
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
votes
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
votes
3answers
137 views
0
votes
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
votes
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
votes
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
vote
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
votes
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.
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1
vote
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:
...
1
vote
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}$$
for some values of the ...
1
vote
1answer
81 views
How to solve this recurrence equation with Mathematica?
I am interested in solving this recurrence relation (equation) with Mathematica code. I am new to Mathematica. I tried RSolve, RSolveValue, AsymptoticRSolveValue commands for this. But I am not ...
3
votes
3answers
259 views
Problem plotting a bifurcation diagram of logistic map
I would like to plot a bifurcation diagram from the logistic map (difference equation) of the type
$$
x_{t+1} = r\,(1-x_{t})\,x_{t}.
$$
The code I used for that was
...
0
votes
1answer
55 views
Making change of variable
I have the following expression
$$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
votes
1answer
83 views
Plot system difference equations
Is this way correct to plot system of difference equation. For example
...
2
votes
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
votes
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. ...
1
vote
0answers
38 views
1
vote
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
votes
2answers
74 views
Trying to generate strings using Recurrence Table
I'm trying to generate strings recursively that look like this:
...
1
vote
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
votes
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
votes
1answer
50 views
Using NIntegrate inside RecurrenceTable
I'm trying to solve self-consistent equations of the form
...
0
votes
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
vote
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
vote
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
votes
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
votes
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 ...
1
vote
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
votes
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
votes
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
votes
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:
...
