Struct bacon_sci::ivp::BDF2

pub struct BDF2<N, S> where
    N: ComplexField,
    S: DimName + DimMin<S, Output = S>,
    DefaultAllocator: Allocator<N, S> + Allocator<N, U3> + Allocator<N, S, S> + Allocator<N, U1, S> + Allocator<(usize, usize), S>,  { /* fields omitted */ }

2nd order backwards differentiation formula method for solving an initial value problem.

Defines the higher and lower order coefficients. Uses BDFInfo for the actual solving.

Examples

use nalgebra::{VectorN, U1};
use bacon_sci::ivp::{BDF2, BDFSolver};
fn derivatives(_t: f64, state: &[f64], _p: &mut ()) -> Result<VectorN<f64, U1>, String> {
    Ok(-VectorN::<f64, U1>::from_column_slice(state))
}

fn example() -> Result<(), String> {
    let bdf = BDF2::new()
        .with_dt_max(0.1)?
        .with_dt_min(0.00001)?
        .with_tolerance(0.00001)?
        .with_start(0.0)?
        .with_end(10.0)?
        .with_initial_conditions(&[1.0])?
        .build();
    let path = bdf.solve_ivp(derivatives, &mut ())?;
    for (time, state) in &path {
        assert!(((-time).exp() - state.column(0)[0]).abs() < 0.001);
    }
    Ok(())
}

Implementations

impl<N, S> BDF2<N, S> where
    N: ComplexField,
    S: DimName + DimMin<S, Output = S>,
    DefaultAllocator: Allocator<N, S> + Allocator<N, U3> + Allocator<N, S, S> + Allocator<N, U1, S> + Allocator<(usize, usize), S>, 

pub fn new() -> Self

Trait Implementations

impl<N, S> BDFSolver<N, S, U3> for BDF2<N, S> where
    N: ComplexField,
    S: DimName + DimMin<S, Output = S>,
    DefaultAllocator: Allocator<N, S> + Allocator<N, U3> + Allocator<N, S, S> + Allocator<N, U1, S> + Allocator<(usize, usize), S>, 

fn higher_coefficients() -> VectorN<N::RealField, U3>

The polynomial interpolation coefficients for the higher-order method. Should start with the coefficient for the derivative function without h, then n - 1. The coefficients for the previous terms should have the sign as if they're on the same side of the = as the next state.

fn lower_coefficients() -> VectorN<N::RealField, U3>

The polynomial interpolation coefficients for the lower-order method. Must be one less in length than higher_coefficients. Should start with the coefficient for the derivative function without h, then n-1. The coefficients for the previous terms should have the sign as if they're on the same side of the = as the next state.

fn solve_ivp<T: Clone, F: FnMut(N::RealField, &[N], &mut T) -> Result<VectorN<N, S>, String>>(
    self,
    f: F,
    params: &mut T
) -> Result<Vec<(N::RealField, VectorN<N, S>)>, String>

Use BDFInfo to solve an initial value problem

fn with_tolerance(mut self: Self, tol: N::RealField) -> Result<Self, String>

Set the error tolerance for this solver.

fn with_dt_max(mut self: Self, max: N::RealField) -> Result<Self, String>

Set the maximum time step for this solver.

fn with_dt_min(mut self: Self, min: N::RealField) -> Result<Self, String>

Set the minimum time step for this solver.

fn with_start(mut self: Self, t_initial: N::RealField) -> Result<Self, String>

Set the initial time for this solver.

fn with_end(mut self: Self, t_final: N::RealField) -> Result<Self, String>

Set the end time for this solver.

fn with_initial_conditions(mut self: Self, start: &[N]) -> Result<Self, String>

Set the initial conditions for this solver.

fn build(mut self: Self) -> Self

Build this solver.

impl<N: Clone, S: Clone> Clone for BDF2<N, S> where
    N: ComplexField,
    S: DimName + DimMin<S, Output = S>,
    DefaultAllocator: Allocator<N, S> + Allocator<N, U3> + Allocator<N, S, S> + Allocator<N, U1, S> + Allocator<(usize, usize), S>, 

fn clone(&self) -> BDF2<N, S>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N: Debug, S: Debug> Debug for BDF2<N, S> where
    N: ComplexField,
    S: DimName + DimMin<S, Output = S>,
    DefaultAllocator: Allocator<N, S> + Allocator<N, U3> + Allocator<N, S, S> + Allocator<N, U1, S> + Allocator<(usize, usize), S>, 

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

Formats the value using the given formatter.

impl<N, S> Default for BDF2<N, S> where
    N: ComplexField,
    S: DimName + DimMin<S, Output = S>,
    DefaultAllocator: Allocator<N, S> + Allocator<N, U3> + Allocator<N, S, S> + Allocator<N, U1, S> + Allocator<(usize, usize), S>, 

fn default() -> Self

Returns the "default value" for a type.

impl<N, S> From<BDF2<N, S>> for BDFInfo<N, S, U3> where
    N: ComplexField,
    S: DimName + DimMin<S, Output = S>,
    DefaultAllocator: Allocator<N, S> + Allocator<N, U3> + Allocator<N, S, S> + Allocator<N, U1, S> + Allocator<(usize, usize), S>, 

fn from(bdf: BDF2<N, S>) -> BDFInfo<N, S, U3>

Performs the conversion.