Numerical Methods for Partial Differential Equations

Course 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)

Lecture Notes

Lecture notes were made available before each class session. Lecture slides were presented during the session. The class was taught concurrently to audiences at both MIT and the National University of Singapore, using audio and video links between the two classrooms, as part of the Singapore-MIT Alliance.

LECTURE SLIDES	LECTURE NOTES
Numerical Methods for Partial Differential Equations (PDF)	(PDF - 1.0 MB)
Finite Difference Discretization of Elliptic Equations: 1D Problem (PDF)	(PDF - 1.6 MB)
Finite Difference Discretization of Elliptic Equations: FD Formulas and Multidimensional Problems (PDF)	(PDF - 1.0 MB)
Finite Differences: Parabolic Problems (PDF)	(PDF)
Solution Methods: Iterative Techniques (PDF)	(PDF - 1.0 MB)
Iterative Methods: Multigrid Techniques (PDF)	(PDF)
Finite Difference Discretization of Hyperbolic Equations: Linear Problems (PDF - 1.7 MB)	(PDF - 2.4 MB)
Hyperbolic Equations: Scalar One-Dimensional Conservation Laws (PDF)	(PDF - 1.4 MB)
Numerical Schemes for Scalar One-Dimensional Conservation Laws (PDF)	(PDF - 1.4 MB)
Finite Element Methods for Elliptic Problems; Variational Formulation: The Poisson Problem (PDF)	(PDF - 1.2 MB)
Discretization of the Poisson Problem in IR1: Formulation (PDF)	(PDF - 1.5 MB)
Discretization of the Poisson Problem in IR1: Theory and Implementation (PDF - 1.9 MB)	(PDF - 2.5 MB)
FEM for the Poisson Problem in IR2 (PDF)	(PDF - 1.6 MB)
Numerical Methods for PEDs, Integral Equation Methods, Lecture 1: Discretization of Boundary Integral Equations (PDF - 1.0 MB)	(PDF)
Numerical Methods for PEDs, Integral Equation Methods, Lecture 2: Numerical Quadrature (PDF)	(PDF)
Numerical Methods for PEDs, Integral Equation Methods, Lecture 3: Discretization Convergence Theory (PDF)	(PDF)
Numerical Methods for PEDs, Integral Equation Methods, Lecture 4: Formulating Boundary Integral Equations (PDF)	(PDF)
Numerical Methods for PEDs, Integral Equation Methods, Lecture 5: First and Second Kind Potential Equations (PDF)
Numerical Methods for PEDs, Integral Equation Methods, Lecture 6: Discretization and Quadrature (PDF)