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

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89 views

Generating Functions with multiple arguments

I want to solve the recurrence of Ackermann function using Generating Function in Mathematica. ...
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85 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 ...
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130 views

An recurrence equation that can be solved in version 7 but not in version 8

Backslide introduced in 8.0, fixed at least in 9.0.1. A friend of mine showed me this code sample: ...
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61 views

Lyapunov Exponent as a function of parameter

I am working at Rossler system and I would like to ask you for some help. This system is described by equations: \begin{array}{ll} \dot{x} = -y - z \\ \dot{y} = x + 0.2y \\ \label{eq:UkladRosSP} \dot{...
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131 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 ...
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23 views

Solving recurrence equation depending on a parameter

I have a recurrence relation which depends on a parameter $t$ and I am trying to solve it using RSolve. This is what I typed: ...
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110 views

How to derive finite-difference scheme automatically on a quite general stencil

Info This question is a generalization of the following one Derivation of numerical scheme for linear transport equation on a variable stencil. Statement of a problem Linear scalar hyperbolic (...
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70 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 ...
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39 views

Recursions where one definition depends on another. How to Block or have local variables?

I have been using Mathematica to solve a second order differential equation using the second order Verlet method. My code looks like: ...
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244 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: ...