# UnivariateTaylorSeriesODESolver(Coef, UTS)¶

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 List UTS -> 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.
ode1: (UTS -> UTS, Coef) -> UTS
ode1(f, c) is the solution to y' = f(y) such that y(a) = c.
ode2: ((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.
ode: (List UTS -> 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).
stFunc1: UTS -> UTS -> 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: (UTS, UTS) -> UTS -> (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: List UTS -> UTS -> List Stream Coef -> Stream Coef
stFuncN(f) is a local function xported due to compiler problem. This function is of no interest to the top-level user.