Numerical solution of initial and boundary value problems in science and engineering: ordinary differential equations; partial differential equations of elliptic, parabolic and hyperbolic type. Topics include Runge Kutta and linear multistep methods, adaptivity, finite elements, finite differences, finite volumes, spectral methods.
Topics to be covered
Initial value problems for ODE: Linear multistep and Runge-Kutta methods, consistency, stability, convergence, stiffness, adaptivity
Geometric integrators: Hamiltonian problems, symplectic methods
Boundary value problems for ODE: Shooting, finite difference, collocation, finite element, and spectral methods
Elliptic PDE: Finite difference, finite element, and spectral methods, consistency and convergence
Hyperbolic and parabolic PDE: Finite difference methods, implicit and explicit time integration
MATH 375 and MATH 387 or permission of the instructor.
Author: Arieh Iserles
Title: A First Course in the Numerical Analysis of Differential Equations
Series: Cambridge Texts in Applied Mathematics
Publisher: Cambridge University Press
Alfio Quarteroni, Riccardo Sacco, and Fausto Saleri. Numerical mathematics. TAM 37. Springer
Randall LeVeque. Finite difference methods for ordinary and partial differential equations. SIAM
Robert Plato. Concise numerical mathematics. GSM 57. AMS
Benedict Leimkuhler and Sebastian Reich. Simulating Hamiltonian dynamics. Cambridge
Burnside Hall 1205
Dr. Gantumur Tsogtgerel
Office: Burnside Hall 1123. Phone: (514) 398-2510. Email: gantumur -at- math.mcgill.ca.
Office hours: T 2:00pm–3:30pm, W 3:00pm–4:30pm, or by appointment.
Both analytical and computational. Assigned and graded roughly every two weeks.
All homework assignments will count towards the final grade. Late homeworks will not be accepted.
In order to receive credit on a homework, you must at least attempt the computational parts of the homework assignments.
The use of Matlab is encouraged; this enables you focus on the algorithms rather than the details of programming.
For computational problems, print out and submit the code that you modified or created (usually the m-file) and the main result (e.g., outputs in text and/or graphics format) only.
There will be a final exam. You are allowed to bring one (double-sided) sheet of hand-written notes to the exam.
The final course grade will be the weighted average of homework 60% and the final exam 40%.