Finite Difference Methods: Linear Systems and Band Matrices

Related lectures (30)

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Explores finite differences for solving linear systems from PDEs iteratively, emphasizing convergence criteria and exercises on singularities.

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

Covers the solution of linear systems using direct methods and the evolution of matrices.

Covers the properties of fundamental solutions and introduces Green's representation formula for solving partial differential equations.

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

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

Covers variational methods in mechanics, focusing on the Ritz-Galerkin method.

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

Explores linear systems, Gaussian elimination, LU decomposition, and matrix types.

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