Differential Equations: Numerical Methods and Simulation Fundamentals · Introduction

Introduction

What this guide covers

Discrete approximation of continuous systems: from the classical analysis of convergence and linear stability to the resolution of rigid and boundary problems.

Overview

Topics covered

Introduction
Differential Equations Numerical Methods
Introduction and Fundamentals of Numerical Simulation
1.1 Formulation of the Initial Value Problem (IVP)
1.2 Picard-Lindelöf Existence and Uniqueness Theorem
1.3 Discretization and Error Fundamentals

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

\begin{cases} \dfrac{dy}{dt} = f(t, y(t)), \quad t \in [t_0, T] \\ y(t_0) = y_0 \end{cases}

View LaTeX source

\begin{cases} 
      \dfrac{dy}{dt} = f(t, y(t)), \quad t \in [t_0, T] \\ 
      y(t_0) = y_0
    \end{cases}