Questions tagged [difference-equations]

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

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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 ...
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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 $$a_{2n-1}=-\sum_{j=1}^{n}{n+j-1\choose 2j-2}a_{n+j-2}, \ a_{0}=-1$$ $$...
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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\...
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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}...
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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 ...
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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: ...
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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] ...
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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)=...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
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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 ...
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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 ...
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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.
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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 ...
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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?
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1answer
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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\}) \\ ...
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2answers
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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 ...
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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. ...
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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: ...
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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 ...
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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 ...
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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-...
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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} ...
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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. ...
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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 ...
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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]+...
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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: ...
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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 ...
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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? ...
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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 $a$, $b$...
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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 ...
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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)=\...
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48 views

Difference Equation system

I am new in Mathematica and I have a very large system of difference equations like: ...
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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] ...
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2answers
137 views

How can I solve a functional equation with domain restrictions?

I have three properties for a function: ...
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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_{...
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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 ...
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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 ...
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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 ...
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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\...
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3answers
179 views

Nonlinear Difference Equations [closed]

How can I plot the nonlinear difference equations?
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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 ...
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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 ...
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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] ...
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1answer
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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 ...
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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. ...
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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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