# Numerical Analysis

## Turing Patterns

I’d like here to share the reoprt I prepared for my final project for the course of Numerical Analysis of PDE here at KAUST. All the code to reproduce the image here presented can be found on this dedicated repo. We are interested in solving numerically the PDE system proposed by Alan Turing in 1952 …

## BEM For Helmholtz Sound-Soft Scattering Problem

During the course of Advanced Numerical Methods for PDE we study the Boundary Elements Method (BEM) for the solution of the Sound Soft Scattering Problem, this post is a remake of the report I presented as part of the exam. We fix the notation that we will use from now on in this report, let …

## Dahlquist Barrier and Symplectic Integrator For Time-Stepping The Wave Equation

So it’s holiday time and I find some times to write, my objective today would be to present and idea regarding how to use the first and the second Dahlquist barrier theorem to prove some theoretical limit of symplectic integrator. Introduction In this first section we will focus our attention to the numerical method to …

## Conjugated Gradient an Optimal Stopping Time Approach

Introduction Suppose that we have a symmetric matrix and our aim is to solve the linear problem to find the exact solution . One of the algorithm widely implemented to perform such task is the conjugated gradient (CG) method. The standard formulation of the CG method is as follow: We define the initial step: . …