Matrices in Difference Equations (1D, 2D, 3D) Video Lecture, MIT

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Mathematical Methods for Engineers II

Lecture 12: Matrices in Difference Equations (1D, 2D, 3D)

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Course Description :

Difference Methods for Ordinary Differential Equations. Finite Differences, Accuracy, Stability, Convergence.One way Wave equation and CFL/ von Neumann Stability. Second order wave equation, wave profiles, heat equation / point source, Finite differences for heat equation. Convection-diffusion/ conservation laws/ analysis/ shocks. Level Set Method. Matrices in difference equations(1D, 2D, 3D). Sparse Matrices.Black-scholes equation. Iterative, General, Multigrid, Conjugate gradient and Krylov Methods. Fast Poisson solver.Weight least squares, calculus of variations/weak form. Error estimates/ projections and many more....

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