_ODE
Symbolic node for the solution value of a first-order initial-value problem.
Represents y(target) where y satisfies y' = rhs(t, y), y(t0) = y0.
Both depVar (the dependent variable y) and indepVar (the independent variable t) are binders: they are excluded from children so that substitute and dependsOn never recurse into them, matching the convention of scalar._Derivative and scalar._Limit. The expression positions rhs, t0, y0, and target are ordinary children and may hold free variables (e.g. a symbolic target keeps the result closed-form).
Evaluation strategy (two tiers, in order):
- Closed-form via
solveODESymbolic: handlesy' = a*y + bfor constant (t-free)a,b; returns a symbolic expression that stays closed-form whent0/y0/targetare free. - Numeric RK4 via
solveODE: foldst0/y0/targetto concrete_Numbers and runs the integrator; returnsRight(_Number(result)). When neither applies,evalreturnsLeft(this)— the fixpoint convention shared with the transform nodes and thescalar._Functionalhierarchy.
Round-trip: toString emits ode(rhs, depVar, indepVar, t0, y0, target), which re-parses to an equivalent node.
Value parameters
- depVar
-
the dependent variable (the unknown function, e.g.
y) - indepVar
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the independent variable (what
yis differentiated against, e.g.t) - rhs
-
the right-hand side
f(t, y)of the ODE - t0
-
the initial time point
- target
-
the point at which the solution is evaluated
- y0
-
the initial value
y(t0)
Attributes
- Graph
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- Supertypes
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trait Serializabletrait Producttrait Equalsclass _Functionaltrait _Expressionclass Objecttrait Matchableclass Any