# Tagged Questions

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### 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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### 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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### 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: ...
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### 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 ...
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### 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. ...
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### 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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### 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 ...
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### 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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### 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 ...
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### 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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### How to find a recurrence relation for a sequence?

I have a sequence given by an explicit formula for n-th term: ...
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### 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: ...
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### 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] ...
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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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### 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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### 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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### Limit as n -> ā for RSolve with Multivariate Recurrence Relation

I'm trying to solve the following when n -> ā: ...
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### 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! ...
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### RSolve: Errors while solving Partial Difference Equation

I tried solving following partial difference equation in Mathematica by typing ...
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### 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 ...
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### 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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### 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 $a_{n} = 2a_{n-1} + 1$: ...
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, ...