ExpressionSpaceODESolver(R, F)¶

utsode.spad line 125 [edit on github]

R: Join(Comparable, IntegralDomain, ConvertibleTo InputForm)
F: FunctionSpace R

Taylor series solutions of explicit ODE's.

seriesSolve: (Equation F, BasicOperator, Equation F, Equation F) -> Any: seriesSolve(eq, y, x=a, y a = b) returns a Taylor series solution of eq around x = a with initial condition y(a) = b. Note: eq must be of the form f(x, y x) y'(x) + g(x, y x) = h(x, y x).

seriesSolve: (Equation F, BasicOperator, Equation F, F) -> Any: seriesSolve(eq, y, x=a, b) is equivalent to seriesSolve(eq, y, x=a, y a = b).

seriesSolve: (Equation F, BasicOperator, Equation F, List F) -> Any: seriesSolve(eq, y, x=a, [b0, ..., b(n-1)]) returns a Taylor series solution of eq around x = a with initial conditions y(a) = b0, y'(a) = b1, y''(a) = b2, …, y(n-1)(a) = b(n-1) eq must be of the form f(x, y x, y'(x), ..., y(n-1)(x)) y(n)(x) + g(x, y x, y'(x), ..., y(n-1)(x)) = h(x, y x, y'(x), ..., y(n-1)(x)).

seriesSolve: (F, BasicOperator, Equation F, Equation F) -> Any: seriesSolve(eq, y, x = a, y a = b) is equivalent to seriesSolve(eq=0, y, x=a, y a = b).

seriesSolve: (F, BasicOperator, Equation F, F) -> Any: seriesSolve(eq, y, x = a, b) is equivalent to seriesSolve(eq = 0, y, x = a, y a = b).

seriesSolve: (F, BasicOperator, Equation F, List F) -> Any: seriesSolve(eq, y, x = a, [b0, ..., bn]) is equivalent to seriesSolve(eq = 0, y, x = a, [b0, ..., b(n-1)]).

seriesSolve: (List Equation F, List BasicOperator, Equation F, List Equation F) -> Any: seriesSolve([eq1, ..., eqn], [y1, ..., yn], x = a, [y1 a = b1, ..., yn a = bn]) returns a taylor series solution of [eq1, ..., eqn] around x = a with initial conditions yi(a) = bi. Note: eqi must be of the form fi(x, y1 x, y2 x, ..., yn x) y1'(x) + gi(x, y1 x, y2 x, ..., yn x) = h(x, y1 x, y2 x, ..., yn x).

seriesSolve: (List Equation F, List BasicOperator, Equation F, List F) -> Any: seriesSolve([eq1, ..., eqn], [y1, ..., yn], x=a, [b1, ..., bn]) is equivalent to seriesSolve([eq1, ..., eqn], [y1, ..., yn], x = a, [y1 a = b1, ..., yn a = bn]).

seriesSolve: (List F, List BasicOperator, Equation F, List Equation F) -> Any: seriesSolve([eq1, ..., eqn], [y1, ..., yn], x = a, [y1 a = b1, ..., yn a = bn]) is equivalent to seriesSolve([eq1=0, ..., eqn=0], [y1, ..., yn], x = a, [y1 a = b1, ..., yn a = bn]).

seriesSolve: (List F, List BasicOperator, Equation F, List F) -> Any: seriesSolve([eq1, ..., eqn], [y1, ..., yn], x=a, [b1, ..., bn]) is equivalent to seriesSolve([eq1=0, ..., eqn=0], [y1, ..., yn], x=a, [b1, ..., bn]).