Merge pull request #61 from master-csmi/24-bibliography-update-for-v1

#24 update bibliograpy and add introduction

References.bib

@@ -1,26 +1,32 @@
 
 @article{lorenz1963deterministic,
-  title={Deterministic nonperiodic flow},
-  author={Lorenz, Edward N},
-  journal={Journal of atmospheric sciences},
-  volume={20},
-  number={2},
-  pages={130--141},
-  year={1963}
+  title   = {Deterministic nonperiodic flow},
+  author  = {Lorenz, Edward N},
+  journal = {Journal of atmospheric sciences},
+  volume  = {20},
+  number  = {2},
+  pages   = {130--141},
+  year    = {1963}
 }
 
 @article{lions2001resolution,
-  title={Résolution d'EDP par un schéma en temps pararéel},
-  author={Lions, Jacques-Louis and Maday, Yvon and Turinici, Gabriel},
-  journal={Comptes Rendus de l'Acad{\'e}mie des Sciences-Series I-Mathematics},
-  volume={332},
-  number={7},
-  pages={661--668},
-  year={2001},
-  publisher={Elsevier}
+  title     = {Résolution d'EDP par un schéma en temps pararéel},
+  author    = {Lions, Jacques-Louis and Maday, Yvon and Turinici, Gabriel},
+  journal   = {Comptes Rendus de l'Acad{\'e}mie des Sciences-Series I-Mathematics},
+  volume    = {332},
+  number    = {7},
+  pages     = {661--668},
+  year      = {2001},
+  publisher = {Elsevier}
 }
 @article{scipy_ode,
-  title={Differential Equations with SciPy – odeint or solve_ivp},
-  author={Daniel Müller-Komorowska},
-  year={February 16, 2021},
+  title  = {Differential Equations with SciPy - odeint or solve_ivp},
+  author = {Daniel Müller-Komorowska},
+  year   = {February 16, 2021}
+}
+
+@misc{cemosis,
+  title  = {Centre for modeling and simulation in Strasbourg},
+  url    = {https://www.cemosis.fr/},
+  author = {Cemosis}
 }

raport.tex

@@ -1,6 +1,8 @@
 \documentclass{article}
 \usepackage{graphicx}
 \usepackage{lipsum}
+\usepackage{url}
+\usepackage{hyperref}
 
 \title{Parareal Algorithm}
 \author{Oussama  BOUHENNICHE, 
@@ -25,7 +27,25 @@
 
 \section{Introduction}
 
-
+    This project, carried out by \href{http://cemosis.fr}{Cemosis} \cite{cemosis} (Centre for Modeling and Simulation in Strasbourg),
+    focuses on the study and implementation of the Parareal algorithm, a parallel method for temporal discretization. 
+
+
+    The primary objective of this project is to investigate the Parareal algorithm and its application in solving partial differential equations (PDEs) using the Cemosis Feel++ framework. 
+
+
+    The project is divided into four sub-objectives. 
+    The first one is to implement the Parareal algorithm sequentially in Python for the Lorenz model, 
+    a set of nonlinear ordinary differential equations. 
+    The second is to implement the Parareal algorithm in parallel in Python for the same Lorenz model. 
+    The third is to implement the Parareal algorithm sequentially in Python for the heat equation using the Feel++ framework. 
+    Finally, the fourth one is to implement the Parareal algorithm in parallel in Python for the heat equation using the Feel++ framework.
+
+
+    Throughout this project, we will utilize Python as the programming language and the Feel++ framework, 
+    which provides a powerful tool for solving PDEs. 
+    By exploring the Parareal algorithm and its implementation in different configurations, 
+    we aim to demonstrate its potential in accelerating the solution of PDEs and its applicability to large-scale simulations.
  \section{Methodology}
  \subsection{Implementing the Lorenz model}