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

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14
votes
1answer
524 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
255 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 ...
9
votes
1answer
365 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
108 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
157 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 ...
6
votes
1answer
233 views

Poisson PDE using FDM in Mathematica

The problem modeled by the Poisson PDE is related to the torsion of prismatic beams and I use the Finite Differences Method. When I use Mathematica to solve it using a quadratic mesh it is working ...
5
votes
3answers
299 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
506 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
249 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
113 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 ...
3
votes
1answer
168 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: ...
3
votes
2answers
152 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
390 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
253 views

Nonlinear recurrence relation

I entered the following recurrence relation into RSolve and it just gave the question back to me. $$a_{n+1} = \frac{(1+a_n +(a_{nāˆ’1})^3)} 3$$ Is there another way to get a formula for the nth term?
3
votes
2answers
200 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
67 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
3answers
72 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
1answer
107 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
0answers
98 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
123 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
75 views

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

I'm trying to solve the following when n -> āˆž: ...
1
vote
2answers
46 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
59 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
73 views

RSolve: Errors while solving Partial Difference Equation

I tried solving following partial difference equation in Mathematica by typing ...
0
votes
1answer
188 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
4answers
148 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
92 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
120 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
91 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
3answers
73 views

Recurrence Relation construction [closed]

How can I go about setting up a recurrence relation where the first 10 values are a constant and the second 10 values are another constant? Ideally, I'd like an efficient way to set ...
0
votes
1answer
61 views

Start indexing at 0 for RSolve without giving an initial value [closed]

I am trying to use RSolve with indexing beginning at 0. Whenever I enter a basic command such as to solve a difference equation such as $a_{n} = 2a_{n-1} + 1$: ...
0
votes
1answer
340 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
571 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
211 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
39 views

plotting the stable and unstable manifolds of a difference equation

I have a 2D non-linear system of difference equations for variables x and y defined as follows: ...
0
votes
0answers
45 views

Is this answer is 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
0answers
11 views

Difference Equation System constructed with SetDelayed: How I can set Non-exploding break?

I have a Difference Equation System constructed with SetDelayed. The system is like as follow. ...
0
votes
0answers
43 views

RSolve: simple 2-variable recurrence

I have a simple recurrence: RSolve[{b[n, k] == b[n - 1, k - 1] + b[n - 1, k]}, b[n, k], {n, k}] But Mathematica cannot handle it, why? When I try to give initial ...
0
votes
0answers
50 views

Calibrating a difference equation system

Sorry for not posting it in the first attempt properly. Consider the simple problem of a first-oder difference equation: ...
0
votes
0answers
64 views

RSolve? How do I Solve these equations using Mathematica

How do I solve these using Mathematica? I'd like to have formula for p[2] to p[n-1]. P[j] ...
0
votes
0answers
38 views

Green functions for recurrence equations

Is it possible to solve recurrence equasions in Mathematica with the use of Green's functions and get a solution as a series?
0
votes
0answers
73 views

RSolve and “the given boundary conditions lead to an empty solution”

I am trying to solve the following recurrence relation: ...
-2
votes
1answer
148 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} ...