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

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3
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80 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 ...
3
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0answers
129 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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0answers
125 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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0answers
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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34 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: ...
0
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0answers
30 views

RSolve fails on a two equation linear system

I am trying to solve the following recurrence relations \begin{align*} \mu r_2-(-t+|\Delta|)r_4&=0,~~~~~~~~~~~~\mu r_{2k}-(-t+|\Delta|)r_{2k+2}+(t+|\Delta|)r_{2k-2}=0\\ -\mu ...
0
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0answers
78 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 ...
0
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79 views

Problem using RSolve

I'm trying to solve the following recurrence relation: ...
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183 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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99 views

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

I am trying to solve the following recurrence relation: ...