LODEstruct
data structure to represent an ODE
Description
Examples
LODEstruct is a data structure to represent an ordinary differential equation. It is created by Slode[DEdetermine].
The entries of an LODEstruct are a set of equations, representing the differential equation, and a set of function names, representing the dependent variables.
The data structure has an attribute table with the following entries:
L - the differential operator in diff notation
rhs - the right hand side of the equation
fun - the name of the dependent variable, for example y
var - the name of the independent variable, for example x
linear - true if L is a linear differential operator and false otherwise
ord - the order of L
coeffs - an Array of coefficients of L
polycfs - true if all coefficients are polynomial and false otherwise
d_max - the maximum degree of polynomial coefficients
If the right hand side is a formal power series in the form Bx+∑n=N∞HnPnx where Bx is a polynomial in x, Pnx is either x−an or 1xn, a is the expansion point, and Hn is an expression in n, then it is represented as a RHSstruct data structure. The entries of an RHSstruct are the right hand side and the independent variable x. In addition, the data structure has an attribute table with following entries:
mvar - the name of the independent variable, x
index - the name of the summation index, n
point - the expansion point a, possibly ∞
M - a nonnegative integer such that series coefficients are equal Hn for all n>M; it satisfies M=maxN−1,degreeBx,x
initial - an Array of M initial series coefficients
H - the expression Hn
P_n - either x−an or 1xn
withSlode:
ode≔diffyx,xx−1−yx=0
ode≔ⅆⅆxyxx−1−yx=0
DEdetermineode,yx
LODEstructⅆⅆxyxx−1−yx=0,yx
attributes
ode1≔diffyx,xx−1−yx=x3+2Sumxnn−3,n=4..∞
ode1≔ⅆⅆxyxx−1−yx=x3+2∑n=4∞xnn−3
DEdetermineode1,yx
LODEstructⅆⅆxyxx−1−yx=x3+2∑n=4∞xnn−3,yx
attributesrhs
See Also
Slode
Slode[DEdetermine]
Download Help Document