Enum Method

pub enum Method {
    Radau5,
    BwEuler,
    FwEuler,
    Rk2,
    Rk3,
    Heun3,
    Rk4,
    Rk4alt,
    MdEuler,
    Merson4,
    Zonneveld4,
    Fehlberg4,
    DoPri5,
    Verner6,
    Fehlberg7,
    DoPri8,
}

Specifies the numerical method to solve (approximate) ODEs

Recommended methods

• Method::DoPri5 for ODE systems and non-stiff problems using moderate tolerances
• Method::DoPri8 for ODE systems and non-stiff problems using strict tolerances
• Method::Radau5 for ODE and DAE systems, possibly stiff, with moderate to strict tolerances

Note: A Stiff problem arises due to a combination of conditions, such as the ODE system equations, the initial values, the stepsize, and the numerical method.

Limitations

• Currently, the only method that can solve DAE systems is Method::Radau5
• Currently, dense output is only available for Method::DoPri5, Method::DoPri8, and Method::Radau5

References

1. E. Hairer, S. P. Nørsett, G. Wanner (2008) Solving Ordinary Differential Equations I. Non-stiff Problems. Second Revised Edition. Corrected 3rd printing 2008. Springer Series in Computational Mathematics, 528p
2. E. Hairer, G. Wanner (2002) Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Second Revised Edition. Corrected 2nd printing 2002. Springer Series in Computational Mathematics, 614p

Variants

Radau5

Radau method (Radau IIA) (implicit, order 5, embedded) for ODEs and DAEs

BwEuler

Backward Euler method (implicit, order 1, unconditionally stable)

FwEuler

Forward Euler method (explicit, order 1, conditionally stable)

Note: This method is interesting for didactic purposes only and should not be used in production codes.

Rk2

Runge (Kutta) method (mid-point) (explicit, order 2)

Reference: page 135 of Hairer, Nørsett, and Wanner (2008)

Rk3

Runge (Kutta) method (explicit, order 3)

Reference: page 135 of Hairer, Nørsett, and Wanner (2008)

Heun3

Heun method (explicit, order 3)

Reference: page 135 of Hairer, Nørsett, and Wanner (2008)

Rk4

“The” Runge-Kutta method (explicit, order 4)

Reference: page 138 of Hairer, Nørsett, and Wanner (2008)

Rk4alt

Runge-Kutta method (alternative) (explicit, order 4, 3/8-Rule)

Reference: page 138 of Hairer, Nørsett, and Wanner (2008)

MdEuler

Modified Euler method (explicit, order 2(1), embedded)

Merson4

Merson method (explicit, order 4(“5”), embedded)

“5” means that the order 5 is for linear equations with constant coefficients; otherwise the method is of order3.

Reference: page 167 of Hairer, Nørsett, and Wanner (2008)

Zonneveld4

Zonneveld method (explicit, order 4(3), embedded)

Reference: page 167 of Hairer, Nørsett, and Wanner (2008)

Fehlberg4

Fehlberg method (explicit, order 4(5), embedded)

Note: this method gives identically zero error estimates for quadrature problems y'=f(x) (see page 180 of ref # 1).

DoPri5

Dormand-Prince method (explicit, order 5(4), embedded)

Verner6

Verner method (explicit, order 6(5), embedded)

Fehlberg7

Fehlberg method (explicit, order 7(8), embedded)

Note: this method gives identically zero error estimates for quadrature problems y'=f(x) (see page 180 of ref # 1).

DoPri8

Dormand-Prince method (explicit, order 8(5,3), embedded)

Implementations

impl Method

pub fn information(&self) -> Information

Returns information about the method

pub fn description(&self) -> &'static str

Returns a description of the method

pub fn erk_methods() -> Vec<Method>

Returns a list of explicit Runge-Kutta methods

Note: FwEuler is also an explicit RK method; however it is not included in this list because it is implemented separately.

Trait Implementations

impl Clone for Method

fn clone(&self) -> Method

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Method

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl PartialEq for Method

fn eq(&self, other: &Method) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Copy for Method

impl Eq for Method

impl StructuralPartialEq for Method