Questions tagged [difference-equations]

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

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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}...
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1answer
128 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
136 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
125 views

Nonlinear Difference Equations [closed]

How can I plot the nonlinear difference equations?
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1answer
29 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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27 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
89 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
51 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 ...
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2answers
80 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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0answers
36 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: ...
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36 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 ...
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1answer
72 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 ...
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3answers
215 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 ...
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1answer
51 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 ...
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1answer
117 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{...
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1answer
58 views

Plot system difference equations

Is this way correct to plot system of difference equation. For example ...
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1answer
93 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 ...
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2answers
121 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 ...
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1answer
55 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 ...
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2answers
136 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 ...
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1answer
73 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. ...
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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 ...
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1answer
38 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 ...
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2answers
72 views

Trying to generate strings using Recurrence Table

I'm trying to generate strings recursively that look like this: ...
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0answers
66 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 ...
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1answer
54 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 ...
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2answers
302 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 ...
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1answer
79 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? ...
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1answer
49 views

Using NIntegrate inside RecurrenceTable

I'm trying to solve self-consistent equations of the form ...
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1answer
92 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 : ...
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52 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 ...
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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? ...
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68 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 ...
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47 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 ...
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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: ...
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4answers
91 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 ...
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0answers
36 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 ...
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151 views

Help with “Coordinate should be a pair of numbers, or a Scaled or Offset form.”

I am plotting the pair of recurrence relations: ...
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RSolve produces a solution which is not complete?

Consider the following solution of a recurrence relation in two variables RSolve[f[x + 1, y] == f[x, y + 1], f[x, y], {x, y}] {{f[x, y] -> C[1][x + y]}} It ...
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Issue plotting a system of recurrence equations

Mathematica noob issues here. So I've got a system of recurrence equations, and following suggestions in other posts,(Plotting two recursive functions) I have the following: ...
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1answer
67 views

Solving a recurrence relation with constraints

I have the following recurrence relation with complex coefficients: c[n] == Sqrt[n-1] c[n-1] + Sqrt[n] c[n+1] I also have the constraint that $\sum_n |c_n|^2 = ...
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1answer
122 views

Solving partial recurrence equation with several recurrence indices

I'm trying to solve a recurrence relation for a function of three variables. It works with 2 variables but not with 3. A simple example is: ...
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1answer
50 views

Problem when using NMinimize in a RecurrenceTable

I have a problem when I'm trying to use NMinimize in my RecurrenceTable, like in this example : ...
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3answers
434 views

Slow computation of recursive sequences

I want to investigate the asymptotic behavior of the following recursive system: ...
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3answers
81 views

What is the fastest way to calculate series from recurrence solutions with no closed form?

I am not very experienced with Mathematica. I want to calculate the series from recurrence solutions. These solutions have no closed-form. I want to improve the approximation and hence need a good ...
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1answer
64 views

recurrence equation

The output of Mathematica is only a copy of the input. What am I doing wrong? ...
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0answers
41 views

How to specify an element of a list when using RecurrenceTable

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 ...
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0answers
56 views

Computing a system of ordinary differential equations with initial condictions over a continuous range [closed]

I have some questions about Mathematica programming and would appreciate if you could help me. I want to solve a system of ordinary differential equations μ '[t] ...

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