Tag for the usage of RSolve, ReccurenceTable, and implementation of finite difference method(FDM) in Mathematica

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17
votes
1answer
652 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, ...
14
votes
1answer
270 views

Mathematica 9 cannot solve a difference equation that Mathematica 8 can

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 Mathematica 9, even after being allowed to run ...
10
votes
1answer
437 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: ...
7
votes
1answer
157 views

How to find a recurrence relation for a sequence?

I have a sequence given by an explicit formula for n-th term: ...
6
votes
1answer
383 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 ...
6
votes
1answer
170 views

RSolve[{y[0] == y0, y[t + 1] == (1 - (t + 1)/100) y[t]}, y[t], t]

When I evaluate this code: RSolve[{y[0] == y0, y[t + 1] == (1 - (t + 1)/100) y[t]}, y[t], t] I get an RSolve::bvnul error. I don't understand why. Yet, if I ...
5
votes
3answers
380 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
600 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 ...
4
votes
5answers
263 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 ...
4
votes
1answer
116 views

RSolve gives a Context::ssle error

I want to solve the following recurrence equation RSolve[{(k + 2) c[k + 2] q^(k + 1) - c[k] == 0}, c[k], k] During calculation in Mathematica I get this ...
4
votes
1answer
243 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: ...
4
votes
1answer
113 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 ...
3
votes
2answers
160 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: $ ...
3
votes
2answers
463 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 ...
3
votes
2answers
303 views

Nonlinear recurrence relation

I entered the following recurrence relation into RSolve and it just gave the question back to me. $$a_{n+1} = \frac{(1+a_n +(a_{n−1})^3)} 3$$ Is there another way to get a formula for the nth term?
3
votes
2answers
222 views

RSolve with assumptions

I want to solve the following non-linear first order difference equation: $$ k_{t+1} = (1-a) k_t^{a} $$ with $0 < a < 1$, and $k_0 = \text{const.}$ . Of course, the solution is easily found, ...
3
votes
0answers
75 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 ...
2
votes
2answers
174 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 ...
2
votes
3answers
120 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 ...
2
votes
3answers
99 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 ...
2
votes
2answers
66 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 ...
2
votes
1answer
83 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
61 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: $$ C_N=N+1+\sum_{0≤k≤N-1}\frac{1}{N}(C_k+C_{N−k−1}) $$ ...
2
votes
1answer
67 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
votes
1answer
128 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 ...
2
votes
2answers
76 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 ...
2
votes
0answers
110 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
1answer
124 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 ...
1
vote
1answer
29 views
1
vote
1answer
77 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 ...
1
vote
2answers
101 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 ...
1
vote
1answer
88 views

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

I'm trying to solve the following when n -> ∞: ...
1
vote
2answers
52 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 ...
1
vote
0answers
65 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 ...
1
vote
0answers
90 views

RSolve: Errors while solving Partial Difference Equation

I tried solving following partial difference equation in Mathematica by typing ...
0
votes
1answer
236 views

I don't understand ListCorrelate! [closed]

I want to solve a PDE equation (like Schrodinger equation) using finite difference in Mathematica. I don't understand what this code does! ...
0
votes
3answers
102 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 ...
0
votes
4answers
153 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: ...
0
votes
1answer
65 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: ...
0
votes
1answer
99 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 ...
0
votes
1answer
36 views

Relationship between input and output coefficients

This is the starting point: ...
0
votes
2answers
102 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: ...
0
votes
1answer
134 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
37 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
votes
1answer
177 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. ...
0
votes
1answer
398 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 ...
0
votes
1answer
678 views

Solving coupled eigenvalue differential equations

I am trying to solve an equation of the form as follows $\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\sin^{2}\left(z\right) & z\\ z & ...
0
votes
2answers
242 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 ...
0
votes
0answers
22 views

Recurrence equation [duplicate]

I need to print the first 10 elements from the string which is a solution of a recurrence equation. If there is a 5 in the elements of the string, then that element should not be printed. For ...
0
votes
0answers
57 views

Problem using RSolve

I'm trying to solve the following recurrence relation: ...