18.336 Numerical Methods of Applied Mathematics II, Spring 2005
Name
18-336Spring-2005/OcwWeb/Mathematics/18-336Spring-2005/CourseHome/index.htm
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13.96 KB
Format
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Checksum (MD5)
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Author(s)
Koev, Plamen S.
Alternative Title
Numerical Methods of Applied Mathematics II
Date Issued
June 2005
Abstract
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.
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
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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