Struct Sri 

pub struct Sri { /* private fields */ }

Kloeden-Platen strong order 1.5 Taylor scheme for scalar autonomous SDEs.

For the Ito SDE dX = f(X) dt + g(X) dW, the step is:

x_{n+1} = x + fdt + gdW + 0.5gg’(dW^2 - dt) [Milstein: L^1 g * I_{(1,1)}] + gf’ * (dtdW - dZ) [L^1 f * I_{(1,0)} term] + (fg’ + 0.5g^2g’‘) * dZ [L^0 g * I_{(0,1)} term] + 0.5ff’ * dt^2 [L^0 f * dt^2/2 term] + (gg’^2 + g^2g’’) * (dW^3 - 3dtdW)/6 [(L^1)^2 g * I_{(1,1,1)}]

where: dZ = integral_0^dt W(s) ds = I_{(0,1)} I_{(1,0)} = dt*dW - dZ I_{(1,1)} = (dW^2 - dt)/2 I_{(1,1,1)} = (dW^3 - 3*dt*dW)/6

All spatial derivatives are approximated by central finite differences with step h.

Reference

Kloeden & Platen, “Numerical Solution of Stochastic Differential Equations”, 1992, Chapter 5.5, the strong Taylor 1.5 scheme (Theorem 5.5.1 / eq. 5.5.4).

Notes

• The I_{(1,1,1)} triple iterated integral is expressible in terms of dW alone: I_{(1,1,1)} = (dW^3 - 3*dt*dW)/6. This is the key 1.5-order correction beyond Milstein.
• For BM (constant diffusion), all correction terms vanish, recovering Euler.
• For GBM (g = sigma*x, g' = sigma, g'' = 0):
  • d111 = g*g'^2 + g^2*g'' = sigma^2*x*sigma = sigma^3*x
  • I_{(1,1,1)} = (dW^3 - 3*dt*dW)/6
  • Combined with the other 1.5 terms, local error reduces to O(dt^2), giving O(dt^{1.5}) globally.
• Requires scalar (1D) SDE with diagonal noise.

Implementations

impl Sri

pub fn new(h: f64) -> Self

Trait Implementations

impl Scheme<f64> for Sri

type Noise = f64

fn step<D, G>( &self, drift: &D, diffusion: &G, x: &f64, t: f64, dt: f64, inc: &Increment<f64>, ) -> f64

where D: Drift<f64>, G: Diffusion<f64, f64>,