Introduction

The current set of implemented and planned time integration methods in each language:

Rust

Exponential integrators:

• ☒ EPI2

• ☒ EPI3

• ☐ EPIRK4

• ☒ EXPRB2

• ☒ EXPRB3

• ☐ PEXPRB4 (parallel exponential rosenbrock order 4)

Classic integrators:

• ☒ RK1,RK2,RK3,RK4

• ☒ Backward Euler

• ☒ BDF2

• ☒ Crank-Nicolson

• ☐ DIRK

• ☐ SDIRK

Python

Exponential integrators:

Jacobian based:

• ☒ EPI2

• ☒ EPI3

• ☐ EPIRK4

• ☒ EXPRB2

• ☒ EXPRB3

• ☒ PEXPRB4

Splitting linear operator based:

• ☒ EXP1

• ☒ EXP2

• ☒ EXP3

• ☐ EXP4

Classic integrators:

• ☒ all explicit and implicit integrators supported by diffrax (through interface with diffrax)

Methods Reference

The following integrators are available through the common high level integrate_wrapper.integrate interface. Different integrators can be specified through the method keyword argument.

method	order	Impl Notes	kwargs	description	Reference
exprb2	2	JAX/python	max_krylov_dim; iom	Exponential Rosenbrock order 2	https://doi.org/10.1137/080717717
exprb3	3	JAX/python	max_krylov_dim; iom	Exponential Rosenbrock order 3	https://doi.org/10.1137/080717717
pexprb4	4	JAX/python	max_krylov_dim; iom	Parallel Exponential Rosenbrock order 4	https://doi.org/10.1016/j.camwa.2016.01.020
epi3	3	JAX/python	max_krylov_dim; iom	Exponential Propagation Iterative order 3	https://doi.org/10.1137/110849961
rk4	4	JAX/python		Explicit RK4
implicit_euler	1	JAX/diffrax		Backward Euler
implicit_esdirk3	3	JAX/diffrax		explicit singly diagonal implicit order 3
dopri5	5	JAX/diffrax		Explicit Dormand-Prince order 5
exprb2_rs	2	Rust	max_krylov_dim; iom	Exponential Rosenbrock order 2	https://doi.org/10.1137/080717717
exprb3_rs	3	Rust	max_krylov_dim; iom	Exponential Rosenbrock order 3	https://doi.org/10.1137/080717717
epi3_rs	3	Rust	max_krylov_dim; iom	Exponential Propagation Iterative order 3	https://doi.org/10.1137/110849961
bdf1_rs	1	Rust		Backward Euler
bdf2_rs	2	Rust		Backward difference formula 2
cn_rs	2	Rust		Crank-Nicolson
rk1_rs	1	Rust		Forward Euler
rk4_rs	4	Rust		Explicit RK4

The Rust-based integrators can be accessed through the common python integrate_wrapper.integrate interface after the Rust-Python bindings are built and installed. Alternatively, the Rust integrator implementations can be used directly from a Rust-based program.