From ac4153cd790dff4b682b8b3a7840d5edb30d4626 Mon Sep 17 00:00:00 2001
From: Aadi <122440845+aadi-bh@users.noreply.github.com>
Date: Wed, 29 Nov 2023 07:33:10 +0530
Subject: [PATCH] Update README.md

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 # Spectral Methods for Hyperbolic Problems
 
-This is an end-semester project to implement parts of the paper "Spectral Methods for Hyperbolic Problems" by Gottlieb and Hesthaven.
+This code implements spectral filtering and Gibbs complimentary basis re-expansion, as outlined in the paper [_Spectral Methods for Hyperbolic Problems_](https://doi.org/10.1016/S0377-0427(00)00510-0) by Gottlieb and Hesthaven.
+
+It is part of an end-semester project, which you can read more about [here](https://aadi.ink/spectral4hyp).
+
+## Install
+Download or clone this repository and then activate your environment 
+before running
+```bash
+pip install -r requirements.txt
+```
+to install the required packages, in case they are not already present.
+
+## Run
+```bash
+python main.py -h
+```
+will show the list of options.
+
+
+| Flag | Explanation | 
+| --- | --- | 
+| `-N` | Number of grid points and Fourier modes (can be used multiple times) |
+| `--pde` | Whether to solve the linear advection or Burgers' equation |
+| `--ggb` | Plot the re-expansion of Fourier coefficients in the basis of Gegenbauer polynomials |
+| '--Lambda' | The value of Lambda (sometimes referred to with alpha) for the Gegenbauer polynomials | 
+| '--exact' | Path to the file containing the exact solution for the specified combination of PDE, initial condition, and final time. |
+
+## Known issues
+The Burgers' equation computes the right solution, but at a wrong speed.
+