# Questions tagged [difference-equations]

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

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### Lyapunov exponents of discrete dynamics with two parameters in one dimension

How can we calculate if we have discrete dynamics with two parameters: f[x_, a_, b_] := Piecewise[{ {1 - a*x, x <= 1/2}, {1 - b*x, x > 1/2} }]
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### Bifurcation diagram with two parameters [duplicate]

I have a question. In Bifurcation diagram of a difference equation I asked for one parameter. And now I am going to tell how do I make a bifurcation diagram of that function with two parameters? I ...
157 views

### Bifurcation diagram of a difference equation

The function is f[x_, a_] := Piecewise[{{x (1 + a - a*x), x <= 1/2}, {x (1 - a + a*x), x > 1/2}}] How to make the bifurcation graphic of it? What ...
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### Solving recurrence equation with variable $x$

Please I want to solve this recurrence equation $$p_n(x)=\frac{1}{x}\left[\frac{n\;}{\sqrt{2 n-1} \sqrt{2 n+1}}p_{n-1}(x)+\frac{(n+1)}{\sqrt{2 n+1} \sqrt{2 n+3}}p_{n+1}(x)\right]$$ $x$ is a variable ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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: ...
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### 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 $q(0)=0$ ...
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### Residues of products

i have the following problem: My function is given by: $(cz^{-1}+aq^{-j}-bq^{-2j}z)\prod_{m=1}^{Q-1}\frac{qz-z_{m}}{z-z_m}+(-cz^{-1}+dq^{j}+bq^{2j}z)\prod_{m=1}^{Q-1}\frac{q^{-1}z-z_{m}}{z-z_m}=E$, ...
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### 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
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### 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 ...
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### 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 ...
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### 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(...
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### 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. ...
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### 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: $12 \rightarrow (1^3 + 2^3) = 9$...
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### DSolve analytical solution of the system equation with two variable

I have a difficulty to solve this system equations: ...
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### 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 $\:\:\:\int_0^r f(x) x^2 dx= \gamma$ ...
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### How to interpret RSolve solution with negative factorial?

I'm having trouble interpreting the following result of RSolve to this difference equation: ...