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Questions tagged [difference-equations]

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

6
votes
2answers
144 views

Find a stable 3-cycle of the sine map

I am trying to find an stable 3-cycle for the sine map $g(x) = a \sin(\pi x)$ but I do not know exactly how to use mathematica to do so. Is there anyone familiar with this? $x$ lies as before ...
-1
votes
1answer
49 views

Error when Solving Recurrence Relation

I would like to analyze the following recurrence relation. $r_i = r_{i-1} - \frac{1}{2} \cdot \sqrt{1 - \frac{4\pi^2\cdot r_{i-1}^2}{n^2}}$ $r_0 = \frac{n}{2\pi}$ I have implemented this as ...
0
votes
0answers
84 views

Is it possible to find the Rössler attractor using only a set of Lyapunov exponents?

Is it possible to use a set of Lyapunov exponents to determine the orbits of the Rössler system? If so, could how would I go about plotting them? EG. Known Unknown
0
votes
0answers
27 views

Trying to solve recursion using rsolve

I'm new to Mathematica, and I'm trying to use RSolve to solve an equation I couldn't do in Matlab, as I got errors there too. This is the system I'm trying to solve:...
0
votes
0answers
21 views
0
votes
1answer
39 views

Help with recurrence relation

I try to solve the following recursion for $n \in \mathbb{N}$. $r_i = r_{i-1} - \frac{1}{2} \cdot \sqrt{1 - \frac{4\pi^2\cdot r_{i-1}^2}{n^2} \cdot \cos^2 \left(\frac{\pi}{n}\right)}$ $r_0 = \...
1
vote
1answer
82 views

Solving recursive equations with RSolve, with constraint and subscripts

I'm trying to solve this set of equations in generality, where $n$ can vary. $\begin{align*} P_{1}&=1-\sum_{i=2}^{n}P_{i}\\ P_{i}&=\frac{c_{i-1}P_{i-1}}{c_{i}+\mu_{i}}, \quad i=2,\dots,n-1\\ ...
0
votes
0answers
29 views

Generating DifferenceRoot Equation

I like to find a difference root equation I use the following methods use for mathematica but I have not get any result Clear[p] ...
0
votes
0answers
23 views

some errors the DiferenceRootReduce

I try to calculate DifferenceRootReduce[( Sqrt[\[Pi]] Gamma[3/2 + k] HypergeometricPFQ[{3/2 + k, -n}, {2 + k}, p])/ Gamma[2 + k], k] but any result ...
2
votes
3answers
49 views

Using rule output as function

Im trying to define a function using the output from RSolve, however i cant get it to work properly. I have a RSolve that output something like: ...
1
vote
1answer
65 views

RSolve and a Piecewise Recurrence + Runtime

This should really be a comment to this answer but I don't have enough rep. I'd like to know how to do the same thing (efficiently - see below) but with $\mod 3$ conditions, i.e. define a[k] to be the ...
1
vote
1answer
38 views

RSolve for three arguments

I would like to find the general expression for a recursive equation: ...
0
votes
1answer
53 views

Recurrence Relation with two variables and boundary conditions

I try to express the following recurrence relation in Mathematica: I am very sorry but for any reason I am not allowed to embed math code here... \begin{align*} x_{1,t} &= \frac{1}{2} x_{1,t-...
1
vote
1answer
83 views

Solution of differential equation and then draw a graph

I have two differential equations: $da/dt = a (.3 a^{-3} + .7)^{1/2}$ and $d \tau /dt = 1/a$. The initial conditions are $t = 0$; $a = 1$ and $\tau = 0$, respectively. How can I solve the ...
4
votes
2answers
129 views

RSolve not reducing for a certain recurrence relation

I'm trying to use RSolve as follows to solve a recurrence relation: ...
3
votes
1answer
59 views

Spectrum of eigen values for coupled differential equations

How do I obtain a spectrum of eigenvalues for my system of coupled differential equations? $$ kf''(\theta) + \epsilon_{1} f(\theta) + a\cos(b \theta + c) g(\theta) = \lambda f(\theta),\\ a\cos(b \...
0
votes
0answers
47 views

Solving a system of recurrence equations

Can anybody help me with the following code for solving a system of nonlinear recurrence equations. When I evaluate the kernel and run it, the output is the same is my input as if the Mathematica is ...
0
votes
0answers
36 views

Recurrence Relation based on Vectors

I am new to Mathematica. I try to solve a recurrence relation based on vectors. So a[n] is a vector for all n (as well as ...
1
vote
0answers
87 views

Solving a recurrence relation with variable coefficients

I am trying to solve this recurrence inequality for $ a_n $, hopefully in terms of $ a_0,a_1,c $ and $ x $, $$(1-x)a_{n+1} \le xa_n + (1+x)a_{n-1} + c\quad\forall\ n\ge1$$ What I tried: RSolve. But ...
1
vote
0answers
40 views

Why does RSolve not give what I expect?

I have a model based on a digraph G. I construct a system of difference equations, modelFull, as seen below. ...
0
votes
0answers
34 views

Avoid Recursion in lag and difference operations

I have a panel data situation and I'm interested in taking lags and differences and using Mathematica to simplify the algebra of the result. Currently I'm working with a model like this: ...
-1
votes
1answer
80 views

How can I solve this systems of differential equation and show a plot?

$$ \frac{\mathrm du}{\mathrm dt} = 1 - u \mathrm e^{\epsilon(8q-1)} $$ $$ \frac{\mathrm dq}{\mathrm dt} = u \mathrm e^{\epsilon (q-1)} - q $$ $ 0 \leq \epsilon \leq 0.1 $ $u(0) = 0$ and $ q(0)=0$ ...
0
votes
0answers
36 views

Residues of products

i have the following problem: My function is given by: $(cz^{-1}+aq^{-j}-bq^{-2j}z)\prod_{m=1}^{Q-1}\frac{qz-z_{m}}{z-z_m}+(-cz^{-1}+dq^{j}+bq^{2j}z)\prod_{m=1}^{Q-1}\frac{q^{-1}z-z_{m}}{z-z_m}=E$, ...
0
votes
1answer
38 views

fisrt 5th iterations of a sequence of functions: integro-differential equations [closed]

Please I am struggling to compute with mathematica the first 5th iterations of the sequence of functions $u[n,t]$ satisfying the integro-differential equation Please help me with the code. Patrick
2
votes
1answer
148 views

Using NIntegrate in Finite Difference Derivative method

I'm trying to solve a second order differential equation using the code given by @xzczd here which is based on this. What this ...
1
vote
0answers
79 views

Zeros of a rational fraction sequence

This is a follow-up of the question Finding a function/differential equation from a 2nd order recurrence relation, I asked yesterday. The reason why I didn't edit the original question was that in ...
2
votes
1answer
72 views

Finding a function/differential equation from a 2nd order recurrence relation

Consider the following 2nd order recurrence relation: $$A_{1}=1,\; A_{2}=z$$ $$A_{n+2}(z)=(b_n+z)A_{n+1}(z)+a_nA_{n}(z),\; n=1,2,3,...$$ where, $$b_n=n\left(n+m+\frac{1}{2}\right),\; a_n=k^2n\left(...
1
vote
1answer
79 views

How to generate a series with recurrence relation? [closed]

I am a beginner in Mathematica and stuck on a problem. I want to generate a series using a recurrence relation, however, I am facing the problem while feeding previous values. ...
8
votes
3answers
207 views

Using Total inside the RecurrenceTable

I would like to perform an operation over IntegerDigits recurrently. The operation is the sum of cubes of the digits, for example: $12 \rightarrow (1^3 + 2^3) = 9$...
2
votes
0answers
117 views

DSolve analytical solution of the system equation with two variable

I have a difficulty to solve this system equations: ...
3
votes
1answer
118 views

Second order 1D equation with integral boundary condition

Is it possible to solve below equation in Mathematica in range $0<x<r$? $f''[x] + \frac{2f'[x]}{x} = -A e^{-B f[x]}$ $ f'[x]|_{x=r}=-\alpha\:\:\:\:\:$ and $\:\:\:\int_0^r f(x) x^2 dx= \gamma$ ...
1
vote
0answers
45 views

How to interpret RSolve solution with negative factorial?

I'm having trouble interpreting the following result of RSolve to this difference equation: ...
5
votes
3answers
109 views

How to find a list of values of recurrence equation?

I tried with RSolve,but it fails: RSolve[{x[n + 1] == n + Sum[j*x[j], {j, 1, n}], x[1] == 1}, x[n], n] Returns unevaluated ...
0
votes
0answers
59 views

DifferenceRoot help

I have being calculate some Series Coefficient and the result was and DifferenceRoot equation but i do not how ...
0
votes
1answer
84 views

Solving recurrence relations

I have the following recurrence system: $$\pi_0 =.25\pi_0 + .25q\pi_1+.5q\pi_2 + q\pi_3 $$ $$\pi_1 =.25\pi_0 + .25q\pi_1+.5\pi_2 + p\pi_3 $$ $$\pi_2 =.25\pi_0 + .25p\pi_1+.5p\pi_2 + 0 $$ $$\pi_3 =....
2
votes
1answer
155 views

Guessing recursion in rational functions

I want to know if there is a package in Mathematica that can give back some recursion given a list of polynomial in $f_{n}(h)$. For example I know there exists package RISC guess that where I give ...
0
votes
0answers
70 views

Solving a boundary-value recurrence relation

I would like to solve a recurrence relation of the form ...
0
votes
0answers
46 views

How many solutions are there in this equation $u_{2018}=0$?

I have a sequence $(u_n)$ so that $u_1=a$ and $u_{n+1}=4u_n (1-u_n)$, for all $n=1,2,\ldots$. How many solutions are there in this equation $u_{2018}=0$? I tried ...
0
votes
0answers
44 views

RSolveValue syntax

Can't see anything wrong with this: sol4 = RSolveValue[{a[n + 1] - 1.2*a[n]*(1 - a[n]) == 0, a[1] ==0.1}, a[n], n] But I just get an echo from Mathematica
3
votes
2answers
85 views

Vector and matrix use in RecurrenceTable

Why is this code snippet that uses matrix and vector elements work? ...
2
votes
1answer
69 views

Recurrence table doesn't like non-linearity?

When I evaluate the following RecurrenceTable expression ...
0
votes
1answer
69 views

Determining the distribution and other characteristics of a variable defined by a recurrence relation

I want to determine the distribution and some other characteristics of a recursive defined variable and need hereby some help/advice. I have the recurrence relation $\qquad X_t = X_{t-1} + \phi (\...
0
votes
1answer
78 views

Sequence equivalent research

I'm studying this series: I know that there is this relation: ($\ell$ is the common limit of the two series) Do you know a Mathematica function that could prove this relation?
0
votes
1answer
39 views

RecurrenceTable with defined functions

I am trying to solve a difference equation using RecurrenceTable as follows. ...
0
votes
2answers
142 views

Solving difference equations involving transcendental functions

v = 0 Solve[Tan[Sqrt[ϵ]]/Sqrt[ϵ] == -Tan[Sqrt[ϵ - v]]/Sqrt[ϵ - v], ϵ] Solve[Tan[Sqrt[a]]/Sqrt[a] == -Tanh[Sqrt[v - a]]/Sqrt[v - a], a] I want to evaluate ...
0
votes
2answers
152 views

Why does this partial differential solution not work?

Here I am trying to solve a simple partial differential equation i.e. $ \frac{\partial^2f}{\partial x^2}+\frac{\partial^2f}{\partial y^2}=6y $ but for some reason it won't solve it. There clearly is a ...
0
votes
1answer
121 views

periodic point of a quadratic map

I am analyzing a discrete dynamic quadratic map. The bifurcation diagram shows the existence of an asymptotic 3- cycle periodic point for a given parameter. But the graphic of the lyapunov exponent ...
0
votes
0answers
49 views

how to To specify initial conditions for a system of ode?

I have the following system of ode: a = {{-3, 1}, {-1, -5}}; eqns = Thread[{y1'[x], y2'[x]} == a.{y1[x], y2[x]} + {1, 1}]; I solved the general solution for a system of ode. However, I cannot ...
3
votes
1answer
119 views

RSolve does not work as expected

Why am I getting error The arguments should be ordered consistently for the following code: ...