UnivariateTaylorSeriesODESolver(Coef, UTS)ΒΆ

utsode.spad line 1 [edit on github]

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.