Questions tagged [difference-equations]

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

Filter by
Sorted by
Tagged with
3
votes
1answer
309 views

Find RSolve solution reflecting special structure of DifferenceRoot[Function[{\[FormalY], \[FormalN]}

RSolve yields a large (multi-page) solution (LeafCount=25891) containing a number of 7F6 (and higher) hypergeometric functions when applied to ...
0
votes
1answer
48 views
3
votes
1answer
73 views

Implementing solution of a system of recurrence relations

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
votes
1answer
36 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 ...
0
votes
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. ...
2
votes
2answers
144 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 ...
2
votes
3answers
222 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
2answers
86 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
votes
1answer
65 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 ...
-1
votes
1answer
144 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
91 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
votes
1answer
28 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
68 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
vote
0answers
41 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
69 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
98 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
votes
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 ...
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
58 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 ...
8
votes
1answer
120 views

Weird RecurrenceTable bug

Bug introduced in 10.0 or earlier and persisting through 12.2 or later The output of RecurrenceTable seems to lose a level when there are more than 250 points and ...
1
vote
0answers
43 views

How to specify an element of a list when using RecurrenceTable [duplicate]

My problem is that I'm trying to get a list of refraction angles in a multilayer structure (for the sake of this example - with two types of refraction indices and eleven layers of them). The code is ...
3
votes
1answer
176 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
378 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
2answers
256 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)=\...
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 ...
0
votes
0answers
45 views

Difference Equation system

I am new in Mathematica and I have a very large system of difference equations like: ...
5
votes
3answers
182 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
131 views
2
votes
1answer
135 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
1answer
49 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_{...
0
votes
0answers
67 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
204 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
196 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 ...
1
vote
1answer
192 views

How do I use RSolve to solve the problem below?

RSolve can't compute the solution. Appears that Mathematica is having a convergence problem. I don't know if the boundary conditions are properly defined... ...
1
vote
1answer
60 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
0answers
40 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
166 views

Nonlinear Difference Equations [closed]

How can I plot the nonlinear difference equations?
0
votes
1answer
33 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 ...
2
votes
1answer
51 views
0
votes
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
93 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] ...
0
votes
2answers
107 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
40 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
45 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
106 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
371 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
65 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 ...

1
2 3 4 5 6