# Questions tagged [difference-equations]

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

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### 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 ...
317 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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### 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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### 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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### 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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### 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 == 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.
66 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 ...
52 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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### 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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### 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, U, etc. ...
61 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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### 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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### 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 ...
41 views