Questions tagged [difference-equations]
Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.
263
questions
0
votes
1answer
28 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
votes
1answer
59 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
1answer
62 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 $$x[n+1]=0.9*y^2[n]/(y[n]+...
1
vote
1answer
34 views
How to print out exclusively even terms of a sequence?
I need to print out the first 20 even-numbered terms of the function $a_{n+1}=\frac{5}{a_n}$. I am capable of printing out each term with this code:
...
3
votes
0answers
54 views
Closed form solution for a differential-difference equation
Considering a differential - difference equation :
$$g (t + 1,s) = \cosh (s) + \frac {\alpha} {t}\sinh (s)\frac {d} {ds} g (t,s)$$
with $g (t, s = 0) =1$, I am looking for a closed form for its ...
1
vote
1answer
84 views
3
votes
1answer
165 views
Using dynamic programming to compute an integer sequence
Let a[n] = n + 1 - a[EulerPhi[n]], n integer > 0. I have Python code that generates the sequence using dynamic programming. How can I achieve the same thing elegantly/idiomatically in Mathematica?
...
4
votes
2answers
304 views
Plotting an image of a discrete dynamical system
I am trying to plot a discrete dynamical system of the form
$$\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}$$
where $a$, $b$...
1
vote
1answer
65 views
problem in solving a non linear differential equation
I'm trying to reslove a differential equation with one of the coefficents depending on the dependent variable, it's a simple dynamic system, with one of the coefficients that can assume 2 values:
The ...
2
votes
2answers
210 views
Chebyshev polynomials
How could I write the Chebyshev polynomial as a function that uses Nest? Also, how could I write it using recursion?
Furthermore, how can I show that $T_n(x)=\...
0
votes
0answers
40 views
Difference Equation system
I am new in Mathematica and I have a very large system of difference equations like:
...
5
votes
3answers
163 views
2 issues with ListDensityPlot
I am using
Mathematica Version Number 12.0.0.0
Platform: Microsoft Windows (64-bit)
The FIRST issue is that the ListDensityPlot is not plotting values of x[Tfinal] ...
4
votes
2answers
116 views
How can I solve a functional equation with domain restrictions?
I have three properties for a function:
...
0
votes
1answer
39 views
Simulation of a recursive stochastic process
I would like to simulate and plot multiple paths of the following stochastic difference equation, for any initial condition $\pi_{0} \in (0,1)$:
$\pi_{t+1} = \gamma \pi_{t}$ with probability $1/3 \pi_{...
2
votes
1answer
127 views
Could anyone help me to compute the following code?
The following code works good when the value of " r < 21 ". But when r > 20, I get the following error message
...
0
votes
0answers
40 views
Trying to implement an algorithm to solve a self-consistent Bloch-Schrodinger Equation
I am trying to understand and to implement an algorithm described by Kunimi-Kato in their supplementary material to solve the self-consistent equation below
$$
\left[\frac{\hbar^{2}}{2m}|\boldsymbol{G}...
0
votes
1answer
152 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
164 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
37 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
146 views
0
votes
1answer
31 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
92 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
56 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
93 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
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
83 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
274 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
58 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
130 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
104 views
Plot system difference equations
Is this way correct to plot system of difference equation. For example
...
2
votes
1answer
116 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
125 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
65 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
140 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
77 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
80 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
44 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
72 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
56 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
325 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
83 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
103 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
57 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 ...
