Lectures related to Finite Differences: Chapter 2

Finite Difference Grids

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Numerical Methods for Boundary Value Problems

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

Other Topics: Techniques for Fluid Interfaces

Explores numerical methods for fluid dynamics and techniques for handling fluid interfaces.

Numerical Methods: Boundary Value Problems

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

Numerical Differentiation and Integration

Covers numerical differentiation and integration techniques using examples and quadrature formulas.

Numerical Methods: Euler Schemes

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

Finite Differences Formulas: Error Analysis

Explores finite differences formulas, error analysis, and numerical experiments in computational mathematics.

Boundary Value Problems: Numerical Methods

Covers the motivation and examples of boundary value problems, the finite difference method, and the approximation of local derivatives.

Numerical Methods: Boundary Value Problems

Explores numerical methods for boundary value problems, including heat diffusion and fluid flow, using finite difference methods.

Finite Elements: Problem with Limits

Covers the application of finite element methods to solve boundary value problems in one dimension.

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.

Advection-Diffusion: Properties and Stability Analysis

Discusses the properties and stability analysis of advection-diffusion equations and the introduction of explicit finite difference schemes.

Convection Diffusion: Equations and Finite Difference Methods

Covers the convection diffusion equation and its numerical approximation methods.

Numerical Differentiation and Integration

Explores numerical differentiation and integration methods, emphasizing the accuracy of finite differences in computing derivatives and integrals.

Finite Elements: Elasticity and Variational Formulation

Explores finite element methods for elasticity problems and variational formulations, emphasizing admissible deformations and numerical implementations.

Finite Differences Method: Error Division and Schemes

Covers error division and schemes for solving differential equations.

Finite Difference Methods: Stability Analysis

Explores the stability analysis of finite difference methods for solving differential equations.

Finite Differences in Advection-Diffusion

Explores the explicit 2-level scheme for advection-diffusion and the convergence of digital solutions.

Boundary Problems in 1D: Finite Differences

Covers chapter 10 on boundary problems in 1D using finite difference methods.