ODETools(F, LODO)

oderf.spad line 535 [edit on github]

• F : Field
• LODO : LinearOrdinaryDifferentialOperatorCategory(F)

ODETools provides tools for the linear ODE solver.

particularSolution : (LODO, F, List(F), Mapping(F, F)) -> Union(F, "failed")

particularSolution(op, g, [f1, ..., fm], I) returns a particular solution h of the equation op y = g where [f1, ..., fm] are linearly independent and op(fi)=0. The value "failed" is returned if no particular solution is found. Note: the method of variations of parameters is used.

variationOfParameters : (LODO, F, List(F)) -> Union(Vector(F), "failed")

variationOfParameters(op, g, [f1, ..., fm]) returns [u1, ..., um] such that a particular solution of the equation op y = g is f1 int(u1) + ... + fm int(um) where [f1, ..., fm] are linearly independent and op(fi)=0. The value "failed" is returned if m < n and no particular solution is found.

wronskianMatrix : List(F) -> Matrix(F)

wronskianMatrix([f1, ..., fn]) returns the n x n matrix m whose i^th row is [f1^(i-1), ..., fn^(i-1)].

wronskianMatrix : (List(F), NonNegativeInteger) -> Matrix(F)

wronskianMatrix([f1, ..., fn], q) returns the q x n matrix m whose i^th row is [f1^(i-1), ..., fn^(i-1)].