Numerical methods for partial differential equations

Lectures: 2 sessions / week, 1.5 hours / session

This course is offered as part of the Singapore-MIT Alliance (SMA), and will be delivered at MIT (by MIT faculty) for MIT students and simultaneously broadcast to the National University of Singapore (NUS) for SMA students. In some cases the roles will reverse: the classes will be delivered at NUS (by NUS SMA faculty) and simultaneously broadcast to MIT.

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.

MIT: 18.03 or 18.06 or equivalent; and familiarity with MATLAB®.

Prof. Jaime Peraire
Prof. Anthony T. Patera
Prof. Jacob White
Prof. Boo Cheong Khoo

Lecture notes are available before class, and archived lecture videos are available after class.

Trefethen, L. N., and D. Bau, III. Numerical Linear Algebra. Philadelphia, PA: SIAM, 1997. ISBN: 9780898713619.

Numerical Methods for Conservation Laws, R. Levecque, Lectures in Mathematics, ETH Zurich, Birkhauser.

Strang, G., and G. J. Fix. Analysis of the Finite Element Method. Upper Saddle River, NJ: Prentice-Hall, 1973. ISBN: 9780130329462.

Quarteroni, A., and A. Valli. Numerical Approximation of Partial Differential Equations. Berlin; New York, NY: Springer-Verlag, 1997. ISBN: 9783540571117 (Berlin: acid-free paper) and ISBN: 9780387571119 (New York: acid-free paper).

Atkinson, K. E. The Numerical Solution of Integral Equations of the Second Kind. Cambridge, UK: Cambridge University Press, 1997. ISBN: 9780521583916 (hardcopy).

Briggs, W. L., et al. A Multigrid Tutorial. 2nd ed. Philadelphia, PA: SIAM, 2000. ISBN: 9780898714623.

Tveito, A., and R. Winther. Introduction to Partial Differential Equations: A Computational Approach. New York, NY: Springer, 1998. ISBN: 9780387983271. (Texts in Applied Mathematics 29, are on reserve at MIT's Barker Library and at NUS's Central Library and SMA Library.)

4 Problem Sets/Projects:

Finite Differences: 25%
Hyperbolic Equations: 20%
Finite Elements: 25%
Boundary Integral Eqs.: 20%
Class Interaction 10%

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