# UnivariateTaylorSeriesODESolver(Coef, UTS)ΒΆ

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.