Questions tagged [difference-equations]
Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.
41
questions with no upvoted or accepted answers
6
votes
0answers
256 views
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,
...
3
votes
0answers
139 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:
...
3
votes
1answer
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
...
3
votes
0answers
250 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{...
3
votes
0answers
144 views
Generating Functions with multiple arguments
I want to solve the recurrence of Ackermann function using Generating Function in Mathematica.
...
3
votes
0answers
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 ...
3
votes
0answers
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:
...
2
votes
0answers
130 views
DSolve analytical solution of the system equation with two variable
I have a difficulty to solve this system equations:
...
2
votes
0answers
361 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 ...
2
votes
0answers
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 ...
1
vote
0answers
37 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 ...
1
vote
0answers
31 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....
1
vote
0answers
111 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 ...
1
vote
0answers
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.
...
1
vote
0answers
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 ...
1
vote
0answers
45 views
How to interpret RSolve solution with negative factorial?
I'm having trouble interpreting the following result of RSolve to this difference equation:
...
1
vote
0answers
93 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:
...
1
vote
0answers
417 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 (...
1
vote
0answers
89 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
...
0
votes
0answers
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[1][m + n]}}
which states that the ...
0
votes
0answers
37 views
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 \...
0
votes
0answers
25 views
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}
}]
0
votes
0answers
30 views
Trying to solve recursion using rsolve
I'm new to Mathematica, and I'm trying to use RSolve to solve an equation I couldn't do in Matlab, as I got errors there too. This is the system I'm trying to solve:...
0
votes
0answers
24 views
0
votes
0answers
32 views
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]
...
0
votes
0answers
23 views
some errors the DiferenceRootReduce
I try to calculate
DifferenceRootReduce[(
Sqrt[\[Pi]]
Gamma[3/2 + k] HypergeometricPFQ[{3/2 + k, -n}, {2 + k}, p])/
Gamma[2 + k], k]
but any result
...
0
votes
0answers
67 views
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 ...
0
votes
0answers
43 views
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 ...
0
votes
0answers
58 views
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:
...
0
votes
0answers
38 views
Residues of products
i have the following problem:
My function is given by:
$(cz^{-1}+aq^{-j}-bq^{-2j}z)\prod_{m=1}^{Q-1}\frac{qz-z_{m}}{z-z_m}+(-cz^{-1}+dq^{j}+bq^{2j}z)\prod_{m=1}^{Q-1}\frac{q^{-1}z-z_{m}}{z-z_m}=E$,
...
0
votes
0answers
68 views
DifferenceRoot help
I have being calculate some Series Coefficient and the result was and DifferenceRoot equation but i do not how
...
0
votes
0answers
111 views
Solving a boundary-value recurrence relation
I would like to solve a recurrence relation of the form
...
0
votes
0answers
47 views
How many solutions are there in this equation $u_{2018}=0$?
I have a sequence $(u_n)$ so that $u_1=a$ and $u_{n+1}=4u_n (1-u_n)$, for all $n=1,2,\ldots$. How many solutions are there in this equation $u_{2018}=0$?
I tried
...
0
votes
0answers
50 views
RSolveValue syntax
Can't see anything wrong with this:
sol4 = RSolveValue[{a[n + 1] - 1.2*a[n]*(1 - a[n]) == 0, a[1] ==0.1},
a[n], n]
But I just get an echo from Mathematica
0
votes
0answers
55 views
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 ...
0
votes
0answers
152 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 ...
0
votes
0answers
30 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 ...
0
votes
0answers
121 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 $zc_{r+2,q}=\frac{\left(q+r+d\right)c_{r+1,q}+\left(r+1\right)c_{r,q}}{d+r+q}$ ...
0
votes
0answers
103 views
Solving recurrence equation using RSolve
I'm trying to solve the following difference equation:
$$
[k(k-1)+s]\,X_k+k\,X_{k-1}=s\,a^k,\;\;k=1,2,\ldots
$$
assuming that $X_0=1$, and $a,s>0$. The obvious
...
0
votes
0answers
110 views
How can I express chains of filters using recurrence relations?
Here's example of what I would typically do in Python to play around with system of custom filters:
...
0
votes
0answers
50 views
Recursions where one definition depends on another. How to Block or have local variables?
I have been using Mathematica to solve a second order differential equation using the second order Verlet method. My code looks like:
...
