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Created by:

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Last updated:

September 23, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

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.

Course Curriculum

  • 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

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Massachusetts Institute of Technology
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