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
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250 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
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0answers
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: ...
3
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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
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0answers
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{...
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0answers
142 views

Generating Functions with multiple arguments

I want to solve the recurrence of Ackermann function using Generating Function in Mathematica. ...
3
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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
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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
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0answers
128 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
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 ...
2
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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
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0answers
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 ...
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0answers
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....
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0answers
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 ...
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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. ...
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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
45 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
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: ...
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0answers
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 (...
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0answers
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 ...
0
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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 ...
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0answers
35 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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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} }]
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0answers
29 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:...
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23 views
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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] ...
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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 ...
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0answers
66 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
42 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
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0answers
54 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
36 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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0answers
66 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
102 views

Solving a boundary-value recurrence relation

I would like to solve a recurrence relation of the form ...
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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 ...
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0answers
49 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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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 ...
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149 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 ...
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0answers
29 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
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0answers
120 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 $zc_{r+2,q}=\frac{\left(q+r+d\right)c_{r+1,q}+\left(r+1\right)c_{r,q}}{d+r+q}$ ...
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0answers
102 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 ...
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0answers
108 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: ...
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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: ...