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This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations
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English
English [CC]
FREE
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Description
In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.
Course content
- Fundamental concepts and examples Unlimited
- Well-posedness and Fourier methods for linear initial value problems Unlimited
- Laplace and Poisson equation Unlimited
- Heat equation, transport equation, wave equation Unlimited
- General finite difference approach and Poisson equation Unlimited
- Elliptic equations and errors, stability, Lax equivalence theorem Unlimited
- Spectral methods Unlimited
- Spectral methods Unlimited
- Elliptic equations and linear systems Unlimited
- Efficient methods for sparse linear systems: Multigrid Unlimited
- Efficient methods for sparse linear systems Unlimited
- Ordinary differential equations Unlimited
- Stability for ODE and von Neumann stability analysis Unlimited
- Advection equation and modified equation Unlimited
- Advection equation and ENO/WENO Unlimited
- Conservation laws Unlimited
- Conservation laws: Numerical methods Unlimited
- Conservation laws: High resolution methods Unlimited
- Operator splitting, fractional steps Unlimited
- Systems of IVP, wave equation, leapfrog, staggered grids Unlimited
- Level set method Unlimited
- Navier-Stokes equation: Finite difference methods Unlimited
- Navier-Stokes equation: Pseudospectral methods Unlimited
- Particle methods Unlimited
Instructor
Massachusetts Institute of Technology
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