Lectures related to Finite Difference Methods: Heat Equation Discretization

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.

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

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

Explores computational methods in quantum physics, emphasizing exact diagonalization and space discretization techniques.

Explores the heat equation in 1D, emphasizing conservation of thermal energy and numerical solution methods.

Explores finite element discretization of the heat equation and its verification process.

Discusses the variational formulation of the heat equation using the finite element method.

Covers the heat equation, its physical interpretation, and numerical methods for solving it.

Explores optimal transport, gradient flows, the implicit Euler scheme, and the heat equation in the context of Dirichlet energy functional.

Explores Fourier analysis, PDEs, historical context, heat equation, Laplace equation, and periodic boundary conditions.

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

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

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

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

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

Explores the maximum principle in the context of the heat equation and the concept of the cylinder.

Covers the finite differences method for approximating solutions to differential equations through discretization and linear systems.

Covers the application of separation of variables method to solve the heat equation.

Explores the application of Fourier transform to PDEs and boundary conditions.

Covers free propagation and the heat equation solution, discussing momentum preservation and Fourier multipliers.