Questions tagged [difference-equations]

Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.

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5
votes
1answer
166 views

Random Variable in Recurrence Function

Following the previously published question, I'm looking for the solution of RecurrenceTable with explicit random variable. For example, something like ...
1
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1answer
202 views

Finite Difference equations - slow computations

The following code I have written runs very slow, in fact, so slow that it does not finish computation. ...
5
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2answers
194 views

Solution to Simultaneous Arithmetic/Geometric Mean Recursion Relations

I'm trying to solve the simultaneous convergent sequences of geometric/arithmetic means where $a_{n+1}=\frac{1}{2}(a_n+b_n)$ and $b_{n+1}=\sqrt{a_nb_n}$ and initial values are $a_0=1+x$ and $b_0=1-x$. ...
2
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1answer
279 views

How to solve coupled complex-valued equations faster and get simplified solution

I have six coupled equations. How to solve these equations symbolically faster in Mathematica. In these equations, variables p,q,x,y are ...
2
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2answers
367 views

Why does Mathematica not evaluate the difference recurrence using `RSolve` or `RecurrenceTable`?

Mathematica does not evaluate the following recurrence of two variables using RSolve and only echoes the input: ...
1
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1answer
91 views

RSolve: Recursive function is not a valid variable

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2
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3answers
125 views

Permutations and recurrence equation

First problem: I need to show all Permutations with length 4 of this elements {x, y, z, w, t} but with this condition: the element z mustn't be after element t. I ...
4
votes
1answer
2k views

Discrete-time Lyapunov exponent plot

I am trying to create a Lyapunov exponent plot as a function of $\alpha$ for two functions: $$ f(x) = (\alpha + 1)x - \alpha x^{3} $$ and a piecewise function given by following Mathematica code: <...
1
vote
1answer
293 views

RSolve with integrations

I want to solve this question with Mathematica. $$T_0(t)=c(t),\quad T_n(t)=a\int_0^t T_{n-1}(s)\, \mathrm{d}s+b(t).$$ Is it possible to solve $T_n(t)$ with RSolve?...
2
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1answer
152 views

Speeding up a differential equation system with nested modulo periodic events

I have the following differential equation system with periodic Events : ...
2
votes
1answer
173 views

Getting the first $n$ terms of a recursion relation

Given a recursion relation, I would like to generate the first $n$ terms (automatically) without having to go term by term. Background Each term is of the form $a_{n}(t)$, that is, $a_{n}$ is a ...
2
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3answers
564 views

Delay difference equation

How can I correctly specify and solve a system of delay difference equations in mathematica similar to NDSolve with regard to delay differential equations? For example if I want to "see" the values ...
3
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1answer
239 views

RSolve and a recurrence relation

In the book An Introduction to the Analysis of Algorithms there is a recurrence relation for the number of compares used in Quicksort algorithm: $$ C_N=N+1+\sum_{0≤k≤N-1}\frac{1}{N}(C_k+C_{N−k−1}) $$ (...
4
votes
1answer
192 views

How can I implement this recurrence equation in Mathematica?

I asked a similar question yesterday but today I realized that I was implementing the wrong function. I have tried changing the implementation but I can't get it to work. Problem: There is a river ...
2
votes
2answers
391 views

How can I express this recurrence function in Mathematica?

\begin{equation} r_{i+1}=r_{i}+V_{i}{\Delta}t \end{equation} Where \begin{equation} V_{i}=(0.01, 0.40) \end{equation} and ${\Delta}t$ is the difference in time. My implementation (this is for ${\...
1
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2answers
388 views

Solving matrix equation

How can I solve the forward equation S[t]=C+A*S[t+1]*(Inverse((I-B*S(t+1)))*A for t=1 to t=10 and ...
0
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1answer
96 views

Can't get solution to a system of recurrence equeations

I would be grateful if someone could help me with this problem. I define two series recursively, thus: ...
3
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2answers
466 views

RSolve with conditional equation

I have the following conditional equation: $f(n) = 1+2 f(n/2)$ when n is even $f(n) = 1+f((n-1)/2)+f((n+1)/2)$ when n is odd I want to represent this as a conditional equation to be used in ...
0
votes
1answer
102 views

Recurrence evaluation at specific index

I have the following set of equations. I want to solve a[n] and f[n] for the indices n=1:5. Note that the relation a[2n+2] involves the derivative of f[2n] and the relation for f[2n+2] involves the ...
0
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1answer
43 views

Relationship between input and output coefficients

This is the starting point: ...
1
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1answer
122 views

Computing a Sequence using Recurrence

I posted a similar question earlier today, but unfortunately I realized after several hours that I over-simplified the problem for this forum. There is a very good answer to the Computing a sequence ...
2
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3answers
175 views

Computing a sequence by recurrence

I am trying to create a list where each element of the list is calculated using the sum of all previous elements of the list and also uses the $N$th element of another list. The initial value of the ...
4
votes
1answer
436 views

Mathematica 10 issue: working with Entities slows down recurrence equations [duplicate]

I was looking at the Mathematica code given at http://community.wolfram.com/groups/-/m/t/326240 where example code is given to simulate the spreading of a supposed Ebola outbreak in Nigeria: ...
1
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2answers
87 views

RecurrenceTable - does it have a solution search option like FindRoot?

I have a second-order non-linear difference equation like $$0=f(x_{t+2},x_{t+1},x_t)$$ where $x_{t+2}$ is implicitly determined. I have tried the code like ...
0
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2answers
133 views

Is this answer true?

I was using Mathematica to get the series solution for Legendre equation. But when I get the recurrence relation and use RSolve: ...
8
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1answer
1k views

Poisson PDE over a irregular region with FDM

The problem modeled by the Poisson PDE is related to the torsion of prismatic beams and I use the Finite Differences Method (FDM). I've managed to solve the equation over a rectangle region with ...
3
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3answers
284 views

Tangled up in sequences and recurrence relations

I took a trip through sequences and recurrence relations and I got tangled up since the documentation didn't help much. I'm sure you can. Given a sequence ...
30
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1answer
2k views

Has this implementation of FDM touched the speed limit of Mathematica?

Still, I'll use the implementation of the 1D FDTD method (you can simply understand it as a kind of explicit finite difference scheme for the Maxwell's equation) as the example. Just for completeness, ...
1
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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 ...
2
votes
1answer
397 views

How can I get DSolve to solve my ODE?

I evaluated DSolve[{x[t] x''[t] + x'[t]^2 - g x[t] == 0, x[0] == 0, x'[0] == 0}, x, t] and the output was {}. But this ODE ...
7
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1answer
397 views

How to find a recurrence relation for a sequence?

I have a sequence given by an explicit formula for n-th term: ...
2
votes
1answer
741 views

FindRoot finds a solution not found by NSolve

I am trying to solve a polynomial equation of higher order with non-integer exponents. When the order of the system is greater than 4, FindRoot provides a correct solution that is not found by NSolve. ...
16
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1answer
328 views

Mathematica 9 cannot solve a difference equation that Mathematica 8 can

Bug introduced in 9.0.1 and fixed in 10.0.0 Consider RSolve[{a[n + 1] == 2 a[n] + n (1 + 2^n), a[1] == 1}, a[n], n] Mathematica 8 can solve this quickly, but ...
0
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4answers
222 views

RSolve fails on a two-equation non-linear system

I have a system of just two recurrence equations, I need to solve them and so I use RSolve: ...
1
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1answer
176 views

Limit as n -> ∞ for RSolve with Multivariate Recurrence Relation

I'm trying to solve the following when n -> ∞: ...
2
votes
1answer
270 views

RSolve: Errors while solving Partial Difference Equation

I tried solving following partial difference equation in Mathematica by typing ...
6
votes
3answers
468 views

RSolve with assumptions

Bug noticed for Mathematica 8 and persisting through 11.3; Submitted to Wolfram, Inc. as CASE:3729158 I want to solve the following non-linear first order difference equation: $$ k_{t+1} = (1-a) k_t^...
1
vote
1answer
142 views

MAP a business cycles model

There is a Business Cycles Map on Phaser 3.0 and I've trying to run it on Mathematica the last four days without succes. The equations are $$ x_1 = (1.0 - a s)x_1 + a \left[s m + g \left(\frac{s m}{...
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 ...
0
votes
1answer
223 views

Explicit, closed formula for recursive integral as a function of the recursive parameter

This is a follow-up of this question/answer. I'm working on a recursive integral more complicated than the one on the linked question, but this one can be used as an example. I would like to obtain ...
0
votes
1answer
676 views

Solving recurrence relationship using iteration

I am trying to create a Mathematica function that basically splits up a continuous function (in this case a physical potential) into steps (strips as it were) and returns the value of the function at ...
3
votes
2answers
200 views

Rook walk and RecurrenceTable in Mathematica

This appears in a combinatorics book: $a(m,n)=2 a(m,n-1)+2 a(m-1,n)-3 a(m-1,n-1)$ It is a recurrence equation for the number of rook walks from $(0,0)$ to $(m,n)$. The initial conditions are: $ a(...
4
votes
5answers
373 views

Can I generate a “piecewise” list from a list in a fast and elegant way?

Suppose we have a number list a: n = 1000000; a = RandomReal[{0, 1}, {n}]; We want to generate a list ...
-2
votes
1answer
184 views

Proof: Convergence of an equation and show the first derivative is bounded

We have the following equation \begin{equation} x(k+1)=\arccos\bigg( -\frac{1}{2(Dr^{\frac {|\sin(2x(k)+\theta)|}{M\sin x(k)\sqrt{A+2B\cos(2x(k)+\theta)}}}+1)} \bigg) \nonumber \end{equation} $A,B,...
7
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3answers
834 views

How can I solve a forward-backward-looking recurrence system?

I would like to (numerically) solve a forward-backward looking recurrence equation in Mathematica. The system is something like: ...
4
votes
1answer
904 views

RSolve Lotka-Volterra: A Closed Form Solution to this Difference Equation?

I would like to solve a difference equation, a Lotka-Volterra difference equation. I tried a model from http://www.stolaf.edu/people/mckelvey/envision.dir/nonDE.lotka-volt.html Using their ...
3
votes
2answers
1k views

RecurrenceTable with a recurrence function of two variables

I have to calculate the cool down process of a regenerative heat exchanger. I solved the problem in Excel before, but now I want to do it with Mathematica. I want to create a table with the variables ...
0
votes
1answer
138 views

Recurrence equations with periodic coefficient

Suppose I have the following recurrence equation: $$ F_{i+1}P_{i+1}+F_iP_i-P_{i+1}+P_i=2J\,, \quad\textrm{with}\quad F_{i+L}=F_i,P_{i+L}=P_i\,. $$ $J$ is constant, $\{P_i\}$ are probabilities with ...
1
vote
2answers
386 views

Random variates in Recurrence Function

I'm completely new to Mathematica and can't seem to find an answer elsewhere so hopefully I can get some help here. I'm trying to plot a recurrence relation, where a random variate is generated at ...
10
votes
1answer
696 views

Is it possible to find a limit of a sequence given by its recurrence relation?

I need to calculate a limit of a sequence given by its recurrence relation. I tried the following: ...