generates a list of values of expr for successive n based on solving the recurrence equations eqns.
generates a list of values of expr over the range of n values specified by nspec.
generates an array of values of expr for successive n1, n2, … .
Details and Options
- The eqns must be recurrence equations whose solutions over the range specified can be determined completely from the initial or boundary values given.
- The eqns can involve objects of the form a[n+i] where i is any fixed integer.
- The range specification nspec can have any of the forms used in Table.
- The following options can be given:
DependentVariables Automatic the list of all dependent variables Method Automatic method to use WorkingPrecision Automatic precision used in internal computations
- With DependentVariables->Automatic, RecurrenceTable attempts to determine the dependent variables by analyzing the equations given.
- With WorkingPrecision->Automatic, results for exact inputs are computed exactly, and for inexact inputs, the precision to use is determined adaptively at each iteration.
- With WorkingPrecision->p, a fixed precision p is used for all iterations.
Examplesopen allclose all
Basic Examples (4)
Ordinary Difference Equations (6)
Partial Difference Equations (2)
Difference-Algebraic Equations (1)
Compare with the symbolic solution given by RSolve:
Generalizations & Extensions (3)
Use DependentVariables to specify the variables when you only want to save some of them:
Logistic Equations (1)
Random Number Generation (1)
Rabbit Fractal (1)
Use ArrayPlot to show the fractal:
Bifurcation Diagram of the Logistic Map (1)
Make a sparse matrix based on applying Count to the iterates for each :
Use ArrayPlot to make the bifurcation diagram:
Compare Numerical Methods for ODEs (1)
Compare the methods for different vector fields with Manipulate: