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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.
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English [CC]
FREE
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Description
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 content
- 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
Instructor
Massachusetts Institute of Technology
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