data structure to represent an ODE

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LODEstruct - data structure to represent an ODE

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

–	var - the name of the independent variable, for example

–	linear - if L is a linear differential operator and otherwise

–	ord - the order of L

–	coeffs - an Array of coefficients of L

–	polycfs - if all coefficients are polynomial and otherwise

–	d_max - the maximum degree of polynomial coefficients

•

If the right hand side is a formal power series in the form B(x)+Sum(H(n)*P[n](x), n = N .. infinity) where is a polynomial in , is either or , is the expansion point, and is an expression in , then it is represented as a RHSstruct data structure. The entries of an RHSstruct are the right hand side and the independent variable . In addition, the data structure has an attribute table with following entries:

–	mvar - the name of the independent variable,

–	index - the name of the summation index,

–	point - the expansion point , possibly

–	M - a nonnegative integer such that series coefficients are equal for all ; it satisfies

–	initial - an Array of initial series coefficients

–	H - the expression

–	P_n - either or

Examples

(1)

(2)

$TABLE([polycfs = true, rhs = 0, ord = 1, L = (diff(y(x), x))*(x-1)-y(x), coeffs = Array(0 .. 1, {0 = -1, 1 = x-1}, datatype = anything, storage = rectangular, order = Fortran_order), linear = true, d_max = 1, var = x, fun = y])$

(3)

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

(4)

$LODEstruct({(diff(y(x), x))*(x-1)-y(x) = x^3+2*(Sum(x^n/(n-3), n = 4 .. infinity))}, {y(x)})$

(5)

>	$attributes(LODEstruct({(diff(y(x), x))(x-1)-y(x) = x^3+2(Sum(x^n/(n-3), n = 4 .. infinity))}, {y(x)}))$

$TABLE([polycfs = true, rhs = RHSstruct(x^3+2*(Sum(x^n/(n-3), n = 4 .. infinity)), x), ord = 1, L = (diff(y(x), x))*(x-1)-y(x), coeffs = Array(0 .. 1, {0 = -1, 1 = x-1}, datatype = anything, storage = rectangular, order = Fortran_order), linear = true, d_max = 1, var = x, fun = y])$

(6)

$attributes((TABLE([polycfs = true, rhs = RHSstruct(x^3+2*Sum(x^n/(n-3),n = 4 .. infinity),x), ord = 1, L = diff(y(x),x)*(x-1)-y(x), coeffs = RTABLE(18446790986281131894,Array(0 .. 1,{0 = -1, 1 = x-1},datatype = anything,storage = rectangular,order = Fortran_order),Array), linear = true, d_max = 1, var = x, fun = y]))['rhs'])$

$TABLE([P_n = x^n, initial = Array(0 .. 3, {3 = 1}, datatype = anything, storage = sparse, order = Fortran_order), mvar = x, index = n, point = 0, M = 3, H = 2/(n-3)])$