Questions tagged [difference-equations]
Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.
55
questions with no upvoted or accepted answers
7
votes
0answers
311 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,
...
4
votes
0answers
159 views
Generating Functions with multiple arguments
I want to solve the recurrence of Ackermann function using Generating Function in Mathematica.
...
3
votes
0answers
72 views
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 ...
3
votes
0answers
29 views
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 ...
3
votes
0answers
164 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
289 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
340 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
106 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
147 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
37 views
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 ...
2
votes
0answers
140 views
DSolve analytical solution of the system equation with two variable
I have a difficulty to solve this system equations:
...
2
votes
0answers
434 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
195 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
Solving a difference equation involving summation expressions-Implicit output
I am trying to solve a difference equation involving summation expression with the following code:
...
1
vote
0answers
38 views
How to study convergence of recurrence relations?
Is there a way to test the convergence of a recurrence relation in Mathematica?
For example does this relation converge:
$$a_{n+1}=a_n \dfrac{n-\dfrac{1}{4}+c^2}{-5+5c^2}$$
for some values of the ...
1
vote
0answers
38 views
1
vote
0answers
79 views
Plot a stable 4-periodic orbit
I have a question guys
In Mathematica how I can plot a stable 4-periodic orbit in the logistic map with giving the four x values for the orbit and find the a value for which it goes through a period ...
1
vote
0answers
70 views
Dirac Operator in de Sitter background
I am attempting to write the Dirac operator in a curved background, and eventually solve the equation as a second order PDE, since I am attempting to bring it into Klein-Gordon form. Essentially what ...
1
vote
0answers
56 views
plot discrete system by mathematica
if I have a discrete system x(n+1)= 0+y , y(n+1)= -0.5x +0
The fixed point (0,0) is center by Jacobian., I do not know how Plot this by using Mathematica code to get center. I am thankful if any one ...
1
vote
0answers
36 views
How to apply RecurrenceTable or Array in two dimensions
This question relates to 104959. How can I solve the following (akward) code by using RecurrenceTable or Array?
...
1
vote
0answers
40 views
RSolve not evaluating when given my system of recurrence equations
I am trying to solve the following system of recurrences with RSolve:
...
1
vote
0answers
25 views
Issue plotting a system of recurrence equations
Mathematica noob issues here. So I've got a system of recurrence equations, and following suggestions in other posts,(Plotting two recursive functions) I have the following:
...
1
vote
0answers
57 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
126 views
Solving a recurrence relation with variable coefficients
I am trying to solve this recurrence inequality for $ a_n $, hopefully in terms of $ a_0ļ¼a_1ļ¼c $ 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
45 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
47 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
110 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
533 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
91 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
45 views
0
votes
0answers
39 views
Difference Equation system
I am new in Mathematica and I have a very large system of difference equations like:
...
0
votes
0answers
39 views
Trying to implement an algorithm to solve a self-consistent Bloch-Schrodinger Equation
I am trying to understand and to implement an algorithm described by Kunimi-Kato in their supplementary material to solve the self-consistent equation below
$$
\left[\frac{\hbar^{2}}{2m}|\boldsymbol{G}...
0
votes
0answers
35 views
Parametrization of twisted pseudospheres types 2 and 3
Among the three types of rotationally symmetric Pseudospherical surfaces $K=-1$ (Beltrami central, type 2 and type 3)
(http://xahlee.info/surface/gallery.html)
we have Dini twist addition term $ b\...
0
votes
0answers
30 views
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 ...
0
votes
0answers
51 views
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 ...
0
votes
0answers
217 views
Help with “Coordinate should be a pair of numbers, or a Scaled or Offset form.”
I am plotting the pair of recurrence relations:
...
0
votes
0answers
40 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
27 views
0
votes
0answers
37 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
80 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
52 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
70 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
81 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
133 views
Solving a boundary-value recurrence relation
I would like to solve a recurrence relation of the form
...
0
votes
0answers
48 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
64 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
59 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
188 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 ...
