From fc38e4184bc7d23e5c22f9c6ff65eb2612aa3a36 Mon Sep 17 00:00:00 2001
From: martinjrobins <martinjrobins@gmail.com>
Date: Tue, 16 Apr 2024 12:59:48 +0000
Subject: [PATCH] #30 update readme

---
 README.md  | 13 ++++++++-----
 src/lib.rs |  5 +++--
 2 files changed, 11 insertions(+), 7 deletions(-)

diff --git a/README.md b/README.md
index 83a3d7f9..a7e5b7ef 100644
--- a/README.md
+++ b/README.md
@@ -17,11 +17,14 @@ implementing the various vector and matrix traits in diffsol.
 
 ## Features
 
-DiffSol has two implementations of the Backward Differentiation Formula
-(BDF) method, one in pure rust, the other wrapping the [Sundials](https://github.com/LLNL/sundials) IDA solver.
-This method is a variable step-size implicit method that is suitable for
-stiff ODEs and semi-explicit DAEs and is similar to the BDF method in MATLAB's
-`ode15s` solver or the `bdf` solver in SciPy's `solve_ivp` function.
+DiffSol implements the following solvers:
+- A variable order Backwards Difference Formulae (BDF) solver, suitable for stiff problems and singular mass matrices.
+- A Singly Diagonally Implicit Runge-Kutta (SDIRK or ESDIRK) solver, suitable for moderately stiff problems and singular mass matrices. You can use your own butcher tableau or use one of the provided (`tr_bdf2` or `esdirk23`).
+- A BDF solver that wraps the IDA solver solver from the [Sundials library](https://github.com/LLNL/sundials) (requires the `sundials` feature). This is similar to the BDF solver above and is include for comparison purposes.
+
+All solvers feature adaptive step-size control to given tolerances, and dense output. 
+For comparison, the BDF solvers are similar to MATLAB's `ode15s` solver or the `bdf` solver in SciPy's `solve_ivp` function. 
+The ESDIRK solver using the provided `tr_bdf2` tableau is similar to MATLAB's `ode23t` solver.
 
 Users can specify the equations to solve in the following ODE form:
 
diff --git a/src/lib.rs b/src/lib.rs
index edd9f60e..6edff2bf 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -12,8 +12,9 @@
 //! [Matrix] trait. You can also use the [sundials](https://computation.llnl.gov/projects/sundials) library for the matrix and vector types (see [SundialsMatrix]).
 //!
 //! To solve the problem, you need to choose a solver. DiffSol provides the following solvers:
-//! - A pure rust Backwards Difference Formulae [Bdf] solver, suitable for stiff problems and singular mass matrices.
-//! - The IDA solver solver from the sundials library ([SundialsIda], requires the `sundials` feature).
+//! - A Backwards Difference Formulae [Bdf] solver, suitable for stiff problems and singular mass matrices.
+//! - A Singly Diagonally Implicit Runge-Kutta (SDIRK or ESDIRK) solver [Sdirk]. You can use your own butcher tableau using [Tableau] or use one of the provided ([Tableau::tr_bdf2], [Tableau::esdirk23]).
+//! - A BDF solver that wraps the IDA solver solver from the sundials library ([SundialsIda], requires the `sundials` feature).
 //!
 //! See the [OdeSolverMethod] trait for a more detailed description of the available methods on each solver.
 //!