From 12509d2c0eb438b9ce431bd6d42d56690ada8cd4 Mon Sep 17 00:00:00 2001
From: Liwei Ji <jiliwei.phys@gmail.com>
Date: Fri, 22 Mar 2024 09:28:32 -0400
Subject: [PATCH] README: Update

---
 README.md | 28 ++++++++++++++++++++++++++++
 1 file changed, 28 insertions(+)

diff --git a/README.md b/README.md
index 5e4b55f..382537f 100644
--- a/README.md
+++ b/README.md
@@ -33,3 +33,31 @@ julia generate_functions.jl
 * [wiki](https://docs.einsteintoolkit.org/et-docs/Prolongation)
 
 * [pseudocode](https://docs.google.com/document/d/1M65w_8keIf6Ypas43YXf1CA-tbuhOssFPpBPlGS1tD0/edit)
+
+## RK4 Steps
+
+* Initialise
+
+* March the first substep for all levels (coarse to fine)
+
+```bash
+ ------
+
+        ------
+               ------
+ ------ ------ ------
+```
+
+* March the other substeps to the same time slice
+
+```julia
+for s = 2:2^(lmax-1)  # from second to final substeps of the finest level
+    for l = 2:lmax  # march all levels execpt the coarest (coarset to fine)
+        if l == lmax || (levs[l].time == levs[l+1].time)
+            if l < lmax
+                Restriction  # from l+1 to l
+            Prolongation  # from l-1 to l
+            rk4(levs[l])
+```
+
+* Restriction all levels