# 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 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, ...
133 views

### 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: ...
263 views

### 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 ...
242 views

### 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{...
142 views

### Generating Functions with multiple arguments

I want to solve the recurrence of Ackermann function using Generating Function in Mathematica. ...
105 views

### 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 ...
146 views

### 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: ...
128 views

### DSolve analytical solution of the system equation with two variable

I have a difficulty to solve this system equations: ...
343 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 ...
192 views

### 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 ...
36 views

### How to specify an element of a list when using RecurrenceTable

My problem is that I'm trying to get a list of refraction angles in a multilayer structure (for the sake of this example - with two types of refraction indices and eleven layers of them). The code is ...
30 views

### Problems with the parametric Recurrence Table

I am trying to construct a minimization program where I have to minimize a function with respect to a matrix. This matrix enters into the optimization program in a convoluted manner together with data....
106 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 ...
43 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. ...
81 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 ...
45 views

### How to interpret RSolve solution with negative factorial?

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

### Solving recurrence equation depending on a parameter

I have a recurrence relation which depends on a parameter $t$ and I am trying to solve it using RSolve. This is what I typed: ...
399 views

### How to derive finite-difference scheme automatically on a quite general stencil

Info This question is a generalization of the following one Derivation of numerical scheme for linear transport equation on a variable stencil. Statement of a problem Linear scalar hyperbolic (...
87 views

### RSolve with simple initial condition

Suppose we have the following equation: $$g_ma_m=r_ma_{m-1}$$ with initial condition $a_L=d$ and $L$ might be negative. The following command ...
21 views

### Does Mathematica find most general recurrence solutions?

Consider e.g. the following recurrence relation solution: RSolve[a[m, n + 1] == a[m + 1, n], a[m, n], {m, n}] {{a[m, n] -> C[m + n]}} which states that the ...
35 views