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LODEstruct

data structure to represent an ODE

 

Description

Examples

Description

• 

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=NHnPnx where Bx is a polynomial in x, Pnx is either xan 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=maxN1,degreeBx,x

– 

initial - an Array of M initial series coefficients

– 

H - the expression Hn

– 

P_n - either xan or 1xn

Examples

with(Slode):

ode := diff(y(x),x)*(x-1)-y(x) = 0;

odeⅆⅆxyxx1yx=0

(1)

DEdetermine(ode,y(x));

LODEstructⅆⅆxyxx1yx=0,yx

(2)

attributes((2));

tabled_max=1,fun=y,L=ⅆⅆxyxx1yx,rhs=0,ord=1,var=x,linear=true,coeffs=Array0..1,0=−1,1=x1,polycfs=true

(3)

ode1 := diff(y(x),x)*(x-1)-y(x) = x^3+2*Sum(x^n/(n-3),n=4..infinity);

ode1ⅆⅆxyxx1yx=x3+2n=4xnn3

(4)

DEdetermine(ode1,y(x));

LODEstructⅆⅆxyxx1yx=x3+2n=4xnn3,yx

(5)

attributes((5));

tabled_max=1,fun=y,L=ⅆⅆxyxx1yx,rhs=RHSstructx3+2n=4xnn3,x,ord=1,var=x,linear=true,coeffs=Array0..1,0=−1,1=x1,polycfs=true

(6)

attributes((6)['rhs']);

tableindex=n,M=3,H=2n3,mvar=x,point=0,P_n=xn,initial=Array0..3,3=1,storage=sparse

(7)

See Also

Slode

Slode[DEdetermine]