UnivariateTaylorSeriesODESolver(Coef, UTS)

utsode.spad line 1 [edit on github]

• Coef : Algebra(Fraction(Integer))
• UTS : UnivariateTaylorSeriesCategory(Coef)

This package provides Taylor series solutions to regular linear or non-linear ordinary differential equations of arbitrary order.

fixedPointExquo : (UTS, UTS) -> UTS

fixedPointExquo(f, g) computes the exact quotient of f and g using a fixed point computation.

mpsode : (List(Coef), List(Mapping(UTS, List(UTS)))) -> List(UTS)

mpsode(r, f) solves the system of differential equations dy[i]/dx =f[i] [x, y[1], y[2], ..., y[n]], y[i](a) = r[i] for i in 1..n.

ode : (Mapping(UTS, List(UTS)), List(Coef)) -> UTS

ode(f, cl) is the solution to y<n>=f(y, y', .., y<n-1>) such that y<i>(a) = cl.(i+1) for i in 0..(n - 1).

ode1 : (Mapping(UTS, UTS), Coef) -> UTS

ode1(f, c) is the solution to y' = f(y) such that y(a) = c.

ode2 : (Mapping(UTS, UTS, UTS), Coef, Coef) -> UTS

ode2(f, c0, c1) is the solution to y'' = f(y, y') such that y(a) = c0 and y'(a) = c1.

stFunc1 : Mapping(UTS, UTS) -> Mapping(Stream(Coef), Stream(Coef))

stFunc1(f) is a local function exported due to compiler problem. This function is of no interest to the top-level user.

stFunc2 : Mapping(UTS, UTS, UTS) -> Mapping(Stream(Coef), Stream(Coef), Stream(Coef))

stFunc2(f) is a local function exported due to compiler problem. This function is of no interest to the top-level user.

stFuncN : Mapping(UTS, List(UTS)) -> Mapping(Stream(Coef), List(Stream(Coef)))

stFuncN(f) is a local function xported due to compiler problem. This function is of no interest to the top-level user.