# Questions tagged [difference-equations]

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

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### RecurrenceTable with defined functions

I am trying to solve a difference equation using RecurrenceTable as follows. ...
246 views

### Solution to differential difference equation

I'm interested in finding the general solution $f(x)$ of the equation: $(1+x)f'(x)+(f(x/2)-f(x))=-1$, $x\ge0$. Can Mathematica help here? For instance, it is easy to verify that the (slightly ...
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### 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 ...
212 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 ...
184 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 ...
147 views

### Solve functional equations which is not exactly recursive

I have the following type of equation : ff[a, b] == alpha[a, b]*ff[0, b] + beta[a, b]*ff[a, 0]+C[a,b] Alpha, beta and C are functions of a and b that I assume ...
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### 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 ...
209 views

### RSolve does not work as expected

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

### WhenEvent for RecurrenceTable

RecurrenceTable is like NDSolve for difference equations, but lacks a lot of its bells and whistles. One thing I'd like to use ...
197 views

### Implementing delay in NestList?

The traditional iterated map can be implemented with NestList, such as the Logistic Map, x[n+1]=rxn, can be implemented with the single line: ...
206 views

### Solving the matrix recurrence in Mathematica

Given matrices, $D, A, B$ --> I have the following recursive relation: $$D_k = A - B^T D^{-1}_{k-1} B , \quad \ k \in \mathbb{N}_+$$ with $D_1 = A_1$. Can a solution $D_k$ to this equation be ...
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### Printing a Solved Recurrence at Arbitrary Values

The code below solves the recurrence $$a_{n+1} = a_{n}d - a_{n-1} + 2 - d$$ where $a_{0} = d^2$ and $a_{1} = d^3 - 2d + 1$. The recurrence is solved as I expect it to be solved. ...
833 views

### Recursion with two variables

Consider the recursion formular $$p_n(k) = (k+1) \,p_{n-1}(k)+(n-k)\,p_{n-1}(k-1)\qquad n\geq 3,$$ for $k=1,2,...,n-2$, with the conditions $$p_n(0)=p_n(n-1)=1\qquad n\geq 2$$ How can I get ...
612 views

### How to simplify output of Series?

The command Series[Sum[Sum[1/(a*b), {b, a, 3 a}], {a, 1, N/Sqrt[3]}, Assumptions -> N > 0], {N, Infinity, 1}] produces a somewhat complicated answer <...
298 views

### RSolve with integrations

I want to solve this question with Mathematica. $$T_0(t)=c(t),\quad T_n(t)=a\int_0^t T_{n-1}(s)\, \mathrm{d}s+b(t).$$ Is it possible to solve $T_n(t)$ with RSolve?...
8k views

### Bifurcation Diagram for 1D Map

Continuing with the same question I have posted earlier I would like to find the equation of the stable fixed point curve using my graph, i.e. from the curve somehow find the equation for $x=f(x)$. I ...
38 views

### Handling recurrence relations

Are there special features in Mathematica for probing a recurrence relation? (dummy example: $f(x) = \prod_{i=1}^N f(x-i)$) Such as, potential simplification, finding base cases, or a visualisation ...
128 views

### set of recursive equations with derivatives

I have the following set of recursive relations $c_{r,q+1}=\frac{\left(2z\partial_{z}+r+1\right)c_{r+1,q}}{d+r+q}$ and $zc_{r+2,q}=\frac{\left(q+r+d\right)c_{r+1,q}+\left(r+1\right)c_{r,q}}{d+r+q}$ ...
138 views

### How can I implement the binomial transform?

How do I implement the binomial transform? I've tried defining a matrix P = Table[(-1)^k Binomial[n, k], {n, 0, m}, {k, 0, m}] and having this act on my ...
182 views

### Why RSOLVE doesn't work here? [closed]

I am trying to use RSOLVE but it doesn't work on very simple examples. My real problem is a little long to explain, but I tried to use RSOLVE on simple case to "test" it and understand how it works ...
1k views

### Using RSolve to solve a recurrence relation

I am attempting to solve this recurrence relation. T[n] = n^(1.5) + T[n - 4] which I believe simplifies to n^(2.5) I ...
349 views

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### Finding Hofstadter's Q-Sequence very slow

I'm trying to find Hofstadter's Q-Sequence. I tried: RSolve[{Q[n] == Q[n - Q[n - 1]] + Q[n - Q[n - 2]], Q[1] == 1, Q[2] == 1}, Q[n], n] but it doesn't work. ...
392 views

### Plotting system of recursive sequences [duplicate]

If I have a system of recursive sequences like x[n+1]=2x[n]+5(y[n])^2 y[n+1]=.5x[n]-3(y[n])^2 How can I plot it as a curves ...
683 views

### Solving recurrent function with 2 variables

My understanding of Mathematica is very limited since I just started using it, I would appreciate any feed back or help. I am trying to find the closed form of a recurrent function with 2 variables: ...
205 views

### Improving my method for solving iterative algebraic equations

So I wish to solve the following $i$ equations for $\eta_i$ $$p(x)+\rho_i z_i + \frac{(u_id)^2}{2(\eta_{i-1}(x)-\eta_i(x))^2}+\rho_i \eta_i(x) = B_i$$ where we have the following definitions and $x$ ...
439 views

### Two dimensional recurrence

My actual problem is a bit more complicated, but let us first assume that we have a recurrence relation of the following type $a_{n,l} = a_{n-1,l} + a_{n-1,l-1} + a_{n,l-1}$ The boundary is given, ...
183 views

### Is RSolve capable of solving the following functional equation? [closed]

I would like to use RSolve (or some other method) to solve the following functional equation: ...
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### Simple linear 2nd order difference equation

I'm trying to run the following code. Unfortunately, there's a mistake in it, which I can't find. Can anyone of you help me? I guess it's very simple. Thanks so much in adavance! ...
138 views

### Problem with using RSolve to solve recurrence equations

Whenever I run the my code, the output of Mathematica is only a copy of the input again. ...
156 views

### How can MovingAverage be used for the solution of nd solve?

The code I used is as below but it doesn't work. Is there anyone who could understand and solve the problem? I want to plot d instead of s.Also, How can I fit a linear function to the d'. ...
162 views

### first order pde [closed]

I wrote below code to solve a first order partial differential equation and find $p(k,t)$ ...
100 views

### RecurrenceTable with vectors

Is there a way to call parts of a vector in RecurrenceTable? This does not work: ...
2k views

### Nonlinear recurrence relation

I entered the following recurrence relation into RSolve and it just gave the question back to me. $$a_{n+1} = \frac{(1+a_n +(a_{n−1})^3)} 3$$ Is there another way ...
56 views

### What is the natural sequence of commands to apply RSolve to a DifferenceRoot[Function? [duplicate]

I am generating some DifferenceRoot[Functions, but to apply RSolve to them, I'm just doing some cutting and pasting from the ...
136 views

### Are there different Method options that can be used with FindSequenceFunction?

The help page states that Method is an option to use with FindSequenceFunction, but I don't find any further information. (There ...