Questions tagged [difference-equations]
Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.
286
questions
0
votes
0answers
44 views
Equal equations or Expressions
I would like to check if equation (Sigmaa22) is the same as equation (stress)
Basically i have 2 equations one is called Sigmaa 22 and the other one is called stress,My problem when i try to check if ...
0
votes
1answer
44 views
Recurrence Table for a specific Recurrence
I wanted to know how can one find an arbitrary number of terms of the non-linear recurrence (using software, like maple)such as
$$a_{2n-1}=-\sum_{j=1}^{n}{n+j-1\choose 2j-2}a_{n+j-2}, \ a_{0}=-1$$
$$...
0
votes
1answer
102 views
Mathematica stuck on partial derivative calculation
I was experimenting polynomial gradient descent on Mathematica, but it got stuck on partial derivative calculation. Formula below:
Traditional Form:
$$
mse = \frac{\sum_{i=1}^{n}\left(y[[i]] - \left(a\...
3
votes
2answers
163 views
Numerical solution of the 2D-spatial nonlinear Allen equation
I would like to solve the 2D-spatial Allen equation in rectangular coordinate, which is a nonlinear reaction-diffusion PDE of the type
$$\partial_{t}u=\epsilon(\partial_{xx}+\partial_{yy})u + u - u^{3}...
0
votes
0answers
71 views
How to Solve this recurrence relation?
When I use RSolve[]
[![enter image description here][1]][1]
It would show this.
I want to solve it to a[n], the function of n & E
How to do that?
The original ...
0
votes
0answers
39 views
Introducing FindRoot in a ReccurrenceTable but problem with the starting point
I would like to introducing FindRoot in a RecurrenceTable, that uses the previous result as a starting point.
My equations are defined as following:
...
0
votes
0answers
83 views
Different solutions for an equation
I have a problem with Mathematica, When I solve this equation in Mathematica and also in wolframalpha I have different solutions [[1]
...
2
votes
1answer
83 views
How do I make a second order differential equation match a difference equation?
I have fitted a difference equation to some data and would now like to find a differential equation that matches the difference equation. The difference equation and differential equation are
$$
y(n)=...
3
votes
1answer
112 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
351 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
votes
1answer
39 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
82 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
votes
1answer
41 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
votes
2answers
154 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
vote
2answers
89 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
73 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
votes
1answer
55 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
votes
1answer
150 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:
$$
\left\{\begin{array}{ll}
\partial_{t} \psi(x,t)-\Delta \psi(x,t)=0, & (x,t)\in (0,1) \times((0, 2) \backslash\{1\}) \\
...
2
votes
2answers
105 views
Computing periodic points of some function
Given a function h[{x_, y_}, b_, c_] := {x^2 + c - b*y, x} for some parameter values b and c ...
0
votes
1answer
34 views
RSolve problem not working
I tried to use Mathematica to find $a_{n}$. But unfortunately, it returned a equation that I can't understand. Here is the code below.
...
0
votes
1answer
80 views
Removing hypergeometric solutions in RSolve [closed]
I am using RSolve to find solutions, but I am only interested in rational solutions.
For example here:
And here is the input code:
...
2
votes
1answer
75 views
Solving recurrent equations with RSolve
I am trying to find a[0] by solving the following system of equations where n can get 1,2,3,...,m-1
...
1
vote
0answers
49 views
Defining general recurrence expression and extracting coefficient
I'm new to Mathematica and I wish to solve a difference equation which is defined by the relation:
$y_{i-1}-2y_{i} +y_{i+1} = f(x_i,y_i),\\y_0 = a, y_n = b.$.
Where $x_i$ is given for all $i$.
I want ...
1
vote
1answer
82 views
Finding fixed points of a system of difference equations
Can anyone help me in finding the fixed points of the systems satisfying all the parameters are real, positive?
$$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
108 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
48 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
65 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 ...
3
votes
3answers
336 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 $$x[n+1]=0.9*y^2[n]/(y[n]+...
1
vote
1answer
40 views
How to print out exclusively even terms of a sequence?
I need to print out the first 20 even-numbered terms of the function $a_{n+1}=\frac{5}{a_n}$. I am capable of printing out each term with this code:
...
3
votes
0answers
63 views
Closed form solution for a differential-difference equation
Considering a differential - difference equation :
$$g (t + 1,s) = \cosh (s) + \frac {\alpha} {t}\sinh (s)\frac {d} {ds} g (t,s)$$
with $g (t, s = 0) =1$, I am looking for a closed form for its ...
1
vote
1answer
94 views
3
votes
1answer
183 views
Using dynamic programming to compute an integer sequence
Let a[n] = n + 1 - a[EulerPhi[n]], n integer > 0. I have Python code that generates the sequence using dynamic programming. How can I achieve the same thing elegantly/idiomatically in Mathematica?
...
4
votes
2answers
428 views
Plotting an image of a discrete dynamical system
I am trying to plot a discrete dynamical system of the form
$$\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
74 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
291 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
48 views
Difference Equation system
I am new in Mathematica and I have a very large system of difference equations like:
...
5
votes
3answers
215 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
137 views
How can I solve a functional equation with domain restrictions?
I have three properties for a function:
...
0
votes
1answer
64 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
votes
1answer
261 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
220 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
46 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
179 views
0
votes
1answer
41 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
34 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
98 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
66 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
116 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
44 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:
...
