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, ...
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159 views

Generating Functions with multiple arguments

I want to solve the recurrence of Ackermann function using Generating Function in Mathematica. ...
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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 ...
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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 ...
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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
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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
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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
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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
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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
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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
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0answers
140 views

DSolve analytical solution of the system equation with two variable

I have a difficulty to solve this system equations: ...
2
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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
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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 ...
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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: ...
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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 ...
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0answers
38 views

General question about RSolveValue and general programming

If I have the following code: ...
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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 ...
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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 ...
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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 ...
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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? ...
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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: ...
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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: ...
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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....
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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_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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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. ...
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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 ...
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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: ...
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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: ...
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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 (...
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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 ...
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0answers
39 views

Difference Equation system

I am new in Mathematica and I have a very large system of difference equations like: ...
0
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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}...
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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\...
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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 ...
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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 ...
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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: ...
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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 \...
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27 views
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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] ...
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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 ...
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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 ...
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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: ...
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0answers
38 views

Residues of products

i have the following problem: My function is given by: $(cz^{-1}+aq^{-j}-bq^{-2j}z)\prod_{m=1}^{Q-1}\frac{qz-z_{m}}{z-z_m}+(-cz^{-1}+dq^{j}+bq^{2j}z)\prod_{m=1}^{Q-1}\frac{q^{-1}z-z_{m}}{z-z_m}=E$, ...
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81 views

DifferenceRoot help

I have being calculate some Series Coefficient and the result was and DifferenceRoot equation but i do not how ...
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0answers
133 views

Solving a boundary-value recurrence relation

I would like to solve a recurrence relation of the form ...
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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 ...
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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
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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 ...
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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 ...