Lectures related to Numerical Methods for PDE

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

Finite Element Method: Basics and Applications

Introduces the Finite Element Method for solving PDEs and demonstrates its application through examples and Comsol Multiphysics.

Introduction to Numerical Methods for PDEs

Covers the numerical approximation of PDEs and examples of nonlinear behavior.

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Parabolic Heat Equation: Modeling and Simulation

Explores the parabolic heat equation evolution and numerical solution methods.

Direction Fields, Euler Methods, Differential Equations

Explores direction fields, Euler methods, and differential equations through practical exercises and stability analysis.

Ordinary Differential Equations: Non-linear Analysis

Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.

Introduction to Partial Differential Equations

Covers the basics of Partial Differential Equations, focusing on heat transfer modeling and numerical solution methods.

Error Estimation in Numerical Methods

Explores error estimation in numerical methods for solving ordinary differential equations, emphasizing the impact of errors on solution accuracy and stability.

System of ODEs

Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Numerical Differentiation: Part 1

Covers numerical differentiation, forward differences, Taylor's expansion, Big O notation, and error minimization.

Numerical Approximation of Partial Differential Equations

Explores numerical methods for solving partial differential equations computationally, emphasizing their importance in predicting various phenomena.

High Order Methods: Space Discretisation

Covers high order methods for space discretisation in linear differential systems.

Numerical Approximation of PDEs

Covers the numerical approximation of PDEs, including Poisson and heat equations, transport phenomena, and incompressible limits.

Finite Differences Method: Error Division and Schemes

Covers error division and schemes for solving differential equations.

Finite Differences and Finite Elements: Variational Formulation

Discusses finite differences and finite elements, focusing on variational formulation and numerical methods in engineering applications.

Finite Difference Method: Approximating Derivatives and Equations

Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Numerical Methods: Euler Schemes

Focuses on Euler schemes for numerical approximation of forces and velocities.