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

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2
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1answer
95 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 ...
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2answers
100 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: ...
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0answers
31 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 ...
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1answer
38 views
2
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2answers
80 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
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1answer
89 views

Speeding up a differential equation system with nested modulo periodic events

I have the following differential equation system with periodic Events : ...
2
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1answer
78 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 ...
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3answers
114 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 ...
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0answers
65 views

Problem using RSolve

I'm trying to solve the following recurrence relation: ...
2
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1answer
74 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
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1answer
125 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 ...
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2answers
191 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 ...
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2answers
112 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 ...
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1answer
75 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: ...
2
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2answers
95 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
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1answer
50 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 ...
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1answer
36 views

Relationship between input and output coefficients

This is the starting point: ...
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1answer
86 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
122 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
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1answer
294 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: ...
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0answers
123 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: ...
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2answers
56 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 ...
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2answers
104 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: ...
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1answer
414 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 ...
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0answers
15 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. ...
3
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3answers
118 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 ...
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0answers
80 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 ...
17
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1answer
702 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, ...
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0answers
68 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
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1answer
133 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 ...
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1answer
175 views

How to find a recurrence relation for a sequence?

I have a sequence given by an explicit formula for n-th term: ...
0
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1answer
243 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. ...
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1answer
274 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 ...
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4answers
155 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: ...
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1answer
91 views

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

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

RSolve: Errors while solving Partial Difference Equation

I tried solving following partial difference equation in Mathematica by typing ...
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0answers
40 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?
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2answers
235 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, ...
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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 ...
3
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0answers
76 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
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1answer
141 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
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1answer
414 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
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2answers
161 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: $ ...
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5answers
267 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 ...
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1answer
162 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} ...
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3answers
421 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: ...
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0answers
84 views

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

I am trying to solve the following recurrence relation: ...
4
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1answer
637 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 ...
0
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1answer
712 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 & ...
3
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2answers
491 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 ...