Basic Nonstiff Methods

This page covers the fundamental explicit methods for solving SDEs. These methods are suitable for non-stiff problems and provide the foundation for more advanced algorithms.

Euler-Maruyama Methods

EM - Euler-Maruyama

EulerHeun - Euler-Heun

LambaEM - Adaptive Euler-Maruyama

LambaEulerHeun - Adaptive Euler-Heun

Milstein Methods

RKMil - Runge-Kutta Milstein

Split Methods

SplitEM - Split Euler-Maruyama

When to Use Basic Methods

Use EM when:

• Computational efficiency is most important
• Problem is not stiff
• Any noise type (most flexible)
• Simple implementation needed

Use EulerHeun when:

• Working in Stratonovich interpretation
• Need slightly better accuracy than EM
• Problem has non-commutative noise

Use LambaEM/LambaEulerHeun when:

• Want adaptive time stepping with basic methods
• Need error control but not high accuracy
• Good balance of simplicity and adaptivity

Use RKMil when:

• Higher accuracy than Euler methods
• Problem has diagonal or scalar noise
• Strong order 1.0 convergence required

These methods form the foundation of stochastic numerical analysis. While higher-order methods often provide better performance, the basic methods are essential for:

• Initial testing and prototyping
• Problems where simplicity is preferred
• Educational purposes
• Fallback options when advanced methods fail