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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4
votes
0
answers
196
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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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3
votes
0
answers
66
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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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3
votes
0
answers
76
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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 ...
- 141
3
votes
0
answers
32
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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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3
votes
0
answers
180
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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:
...
- 2,957
3
votes
1
answer
339
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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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3
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0
answers
511
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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{...
- 59
3
votes
0
answers
112
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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 ...
- 6,938
3
votes
0
answers
149
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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:
...
- 54.1k
2
votes
0
answers
48
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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 ...
- 18k
2
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0
answers
142
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DSolve analytical solution of the system equation with two variable
I have a difficulty to solve this system equations:
...
- 71
2
votes
0
answers
567
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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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2
votes
0
answers
208
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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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1
vote
0
answers
62
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Solving a 2D recurrence diagonal-by-diagonal
I have a 3D recurrence relation -- which I know can be hard for Mathematica to work with, so I boiled it down to 2D.
We have two functions, $f_1(i,j)$, $f_2(i,j)$ defined on the state space $\{(i,j) | ...
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1
vote
0
answers
54
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Defining general recurrence expression and extracting coefficient
I'm new to Mathematica and I wish to solve a difference equation which is defined by the relation:
$y_{i-1}-2y_{i} +y_{i+1} = f(x_i,y_i),\\y_0 = a, y_n = b.$.
Where $x_i$ is given for all $i$.
I want ...
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0
answers
47
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Solving a difference equation involving summation expressions-Implicit output
I am trying to solve a difference equation involving summation expression with the following code:
...
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1
vote
0
answers
63
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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 ...
- 6,164
1
vote
0
answers
47
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1
vote
0
answers
163
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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 ...
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1
vote
0
answers
111
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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 ...
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1
vote
0
answers
68
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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 ...
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1
vote
0
answers
44
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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?
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1
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answers
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RSolve not evaluating when given my system of recurrence equations
I am trying to solve the following system of recurrences with RSolve:
...
- 141
1
vote
0
answers
32
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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:
...
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1
vote
0
answers
72
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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....
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1
vote
0
answers
159
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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 ...
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1
vote
0
answers
50
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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.
...
- 4,401
1
vote
0
answers
82
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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 ...
- 1,504
1
vote
0
answers
51
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How to interpret RSolve solution with negative factorial?
I'm having trouble interpreting the following result of RSolve to this difference equation:
...
- 19.2k
1
vote
0
answers
122
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:
...
- 111
1
vote
0
answers
621
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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 (...
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1
vote
0
answers
93
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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
...
- 1,189
0
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0
answers
38
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Progress Indication for RecurrenceTable
I am trying to figure out how to implement progress indicator in RecurrenceTable. I have a complicated code within the With function that contains recurrence table. A simple code will suffice say,
<...
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47
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RSolve[] gives error RSolve::litarg when solving demo equations from the official documentation
The official documentation of RSolve[] (specifically, in the fifth paragraph of the seciton "Details and Options") states that:
The specification a∈Vectors[m] or a∈Matrices[{m,p}] can be ...
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0
answers
49
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Equal equations or Expressions
I would like to check if equation (Sigmaa22) is the same as equation (stress)
Basically i have 2 equations one is called Sigmaa 22 and the other one is called stress,My problem when i try to check if ...
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88
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How to Solve this recurrence relation?
When I use RSolve[]
[![enter image description here][1]][1]
It would show this.
I want to solve it to a[n], the function of n & E
How to do that?
The original ...
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0
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0
answers
43
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Introducing FindRoot in a ReccurrenceTable but problem with the starting point
I would like to introducing FindRoot in a RecurrenceTable, that uses the previous result as a starting point.
My equations are defined as following:
...
- 1,225
0
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0
answers
84
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Different solutions for an equation
I have a problem with Mathematica, When I solve this equation in Mathematica and also in wolframalpha I have different solutions [[1]
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53
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Difference Equation system
I am new in Mathematica and I have a very large system of difference equations like:
...
0
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0
answers
53
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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\...
- 2,820
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votes
0
answers
35
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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 ...
- 1,847
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88
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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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0
answers
852
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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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0
answers
54
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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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0
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33
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0
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0
answers
47
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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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0
votes
0
answers
86
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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 ...
- 47
0
votes
0
answers
67
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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 ...
- 105
0
votes
0
answers
78
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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:
...
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