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Last updated:

November 4, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

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Description

A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields.

Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.

This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations).

Course Curriculum

  • Numerical Methods for Partial Differential Equations Unlimited
  • Finite Difference Discretization of Elliptic Equations: 1D Problem Unlimited
  • Finite Difference Discretization of Elliptic Equations: FD Formulas and Multidimensional Problems Unlimited
  • Finite Differences: Parabolic Problems Unlimited
  • Solution Methods: Iterative Techniques Unlimited
  • Iterative Methods: Multigrid Techniques Unlimited
  • Finite Difference Discretization of Hyperbolic Equations: Linear Problems Unlimited
  • Hyperbolic Equations: Scalar One-Dimensional Conservation Laws Unlimited
  • Numerical Schemes for Scalar One-Dimensional Conservation Laws Unlimited
  • Finite Element Methods for Elliptic Problems; Variational Formulation: The Poisson Problem Unlimited
  • Discretization of the Poisson Problem in IR1: Formulation Unlimited
  • Discretization of the Poisson Problem in IR1: Theory and Implementation Unlimited
  • FEM for the Poisson Problem in IR2 Unlimited
  • Numerical Methods for PDEs, Integral Equation Methods, Lecture 1: Discretization of Boundary Integral Equations Unlimited
  • Numerical Methods for PDEs, Integral Equation Methods, Lecture 2: Numerical Quadrature Unlimited
  • Numerical Methods for PDEs, Integral Equation Methods, Lecture 3: Discretization Convergence Theory Unlimited
  • Numerical Methods for PDEs, Integral Equation Methods, Lecture 4: Formulating Boundary Integral Equations Unlimited
  • Numerical Methods for PDEs, Integral Equation Methods, Lecture 5: First and Second Kind Potential Equations Unlimited
  • Numerical Methods for PDEs, Integral Equation Methods, Lecture 6: Discretization and Quadrature Unlimited

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Massachusetts Institute of Technology
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