18.336 Numerical Methods of Applied Mathematics II, Spring 2005

18.336 Numerical Methods of Applied Mathematics II, Spring 2005

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Advanced introduction to applications and theory of numerical methods for solution of differential equations, especially of physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. Topics include finite differences, spectral methods, finit...

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Bibliographic Details
Main Author: Koev, Plamen S.
Other Authors: Massachusetts Institute of Technology. Department of Mathematics
Format: Learning Object
Language:en-US
Published: 2010
Subjects:
Linear systems
Fast Fourier Transform
Wave equation
Von Neumann analysis
Conditions for stability
Dissipation
Multistep schemes
Dispersion
Group Velocity
Propagation of Wave Packets
Parabolic Equations
The Du Fort Frankel Scheme
Convection-Diffusion equation
ADI Methods
Elliptic Equations
Jacobi, Gauss-Seidel and SOR(w)
ODEs
finite differences
spectral methods
well-posedness and stability
boundary and nonlinear instabilities
Finite Difference Schemes
Partial Differential Equations
270301
Applied Mathematics
Online Access:http://hdl.handle.net/1721.1/56567
Description
Summary:Advanced introduction to applications and theory of numerical methods for solution of differential equations, especially of physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. Topics include finite differences, spectral methods, finite elements, well-posedness and stability, particle methods and lattice gases, boundary and nonlinear instabilities. From the course home page: Course Description This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.

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