# Questions tagged [difference-equations]

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

62 questions with no upvoted or accepted answers
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### How to solve this multivariate recurrence with Mathematica?

I would like to solve this recurrence relation: $a_{m,n}=a_{m-1,n}+a_{m,n-1}$ with $a_{0,0}=0, a_{m,0}=1, a_{0,n}=1$ for all $m\neq0$ and $n\neq0$ That's resembles the Tartaglia/Pascal's triangle, ...
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### Generating Functions with multiple arguments

I want to solve the recurrence of Ackermann function using Generating Function in Mathematica. ...
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### Closed form solution for a differential-difference equation

Considering a differential - difference equation : $$g (t + 1,s) = \cosh (s) + \frac {\alpha} {t}\sinh (s)\frac {d} {ds} g (t,s)$$ with $g (t, s = 0) =1$, I am looking for a closed form for its ...
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### 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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### 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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### Coupled parabolic differential equations with time delay

Is it possible for NDSolve to solve delay partial differential equations with simple Neumann boundary conditions? An example I have is as below: ...
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### Find RSolve solution reflecting special structure of DifferenceRoot[Function[{\[FormalY], \[FormalN]}

RSolve yields a large (multi-page) solution (LeafCount=25891) containing a number of 7F6 (and higher) hypergeometric functions when applied to ...
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### Lyapunov Exponent as a function of parameter

I am working at Rossler system and I would like to ask you for some help. This system is described by equations: \begin{array}{ll} \dot{x} = -y - z \\ \dot{y} = x + 0.2y \\ \label{eq:UkladRosSP} \dot{...
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### How to combine DifferenceRoot objects for odd and even-indexed terms

I'm trying to analyze a certain infinite sequence $S$, indexed by positive integers starting from $1$. It can be split into two subsequences: $S^{odd}$ by removing all even-indexed elements and ...
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### A recurrence equation that can be solved in version 7 but not in version 8

Backslide introduced in 8.0, fixed at least in 9.0.1. A friend of mine showed me this code sample: ...
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### 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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### DSolve analytical solution of the system equation with two variable

I have a difficulty to solve this system equations: ...
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567 views

### Quasinormal modes with Mathematica

I want to compute the quasi-normal modes for the Kerr-AdS black hole, so basically after decoupling the angular and the radial equation, I have troubles to compute the separation constant and also the ...
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### RSolve and incomplete gamma function

I am interested in how Mathematica uses the incomplete gamma function to solve difference equations. For example, if we have this inhomogeneous, 2nd order equation and use ...
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### 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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### 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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### 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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### How to find the value in which an expression becomes greater than another

I have the following expressions: $\Delta \sigma_1=\frac{2 \gamma ^2 \left(\text{$\sigma $Y} \log \left(\frac{\gamma }{\alpha }\right)+\text{pe}\right)}{\left(\gamma ^2-1\right) \rho ^2}$ \$\Delta \...
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### 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] ...
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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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