The ode_def macro

@ode_def [name] begin
    dstate = expression
    # additional derivative assignments
end parameter_names...

Define a parameterized ordinary differential equation and return an SciMLBase.AbstractParameterizedFunction suitable for an ODEProblem. The macro generates in-place and out-of-place right-hand sides, a time gradient, and a Jacobian through ModelingToolkit.

Arguments

• name: optional name for the generated function type. Omit it to return an anonymous parameterized function.
• derivative assignments: a begin block whose statements have the form dstate = expression. The identifier after d becomes a state variable. The independent variable is t.
• parameter_names...: symbols used as parameters in the derivative expressions. Their numerical values are supplied by the problem's p argument.

Keywords

This macro does not accept keyword arguments.

Returns

An AbstractParameterizedFunction with generated f, tgrad, and jac methods. Pass it as the f argument of an ODEProblem.

Examples

lotka_volterra = @ode_def begin
    dx = a * x - b * x * y
    dy = -c * y + d * x * y
end a b c d

@ode_def_bare [name] begin
    dstate = expression
    # additional derivative assignments
end parameter_names...

Define a parameterized ODE without generating symbolic derivative functions.

Arguments

• name: optional name for the generated function type.
• derivative assignments: the same assignment-based ODE DSL accepted by @ode_def.
• parameter_names...: symbols used as parameters in the expressions.

Keywords

This macro does not accept keyword arguments.

Returns

An AbstractParameterizedFunction with a generated right-hand side and nothing for generated derivative-function fields. Use it when symbolic Jacobian and time gradient generation is unnecessary.

Examples

linear = @ode_def_bare begin
    dx = a * x
end a

@ode_def_all [name] begin
    dstate = expression
    # additional derivative assignments
end parameter_names...

Define a parameterized ODE and request every derivative function supported by this DSL, including factorized W functions for small systems.

Arguments

• name: optional name for the generated function type.
• derivative assignments: the same assignment-based ODE DSL accepted by @ode_def.
• parameter_names...: symbols used as parameters in the expressions.

Keywords

This macro does not accept keyword arguments.

Returns

An AbstractParameterizedFunction with generated right-hand side, time-gradient, Jacobian, and supported factorized-W functions.

Examples

linear = @ode_def_all begin
    dx = a * x
end a