Instructor: Jon Wilkening

GSI: Andrew Shi

Lectures: a mix of asynchronous lectures and a weekly zoom meeting on Thursdays, 5:10-6 PM

Zoom link (for lectures and office hours): see bCourses

Office Hours: Tues 12-1 PM, plus another hour TBA

Prerequisites: Undergraduate Analysis (104), Linear Algebra (110), Numerical Analysis (128A)

Required Texts:
Jon Wilkening, Hand-written lecture notes for Math 228A from 2007

Recommended Reading:
Arieh Iserles, A First Course in the Numerical Analysis of Differential Equations
Hairer/Norsett/Wanner, Solving Ordinary Differential Equations, Volume I

Syllabus: We will cover thoery and practical methods for solving systems of ordinary differential equations. We will discuss Runge-Kutta and multistep methods, stability theory, Richardson extrapolation, stiff equations and high-order time-stepping methods. We will then transition to ODE methods for PDE applications, including the Method of Lines, Implicit/Explicit methods, exponential time-differencing methods and spectral deferred correction methods. The course will conclude with a study of numerical methods for boundary value problems. Here is a tentative schedule:

• weeks 1-2. Analysis of Euler's method and the trapezoidal rule; Richardson extrapolation
• weeks 3-5. Order and stability of multistep methods
• weeks 6-7. Runge-Kutta methods, order conditions, embedded methods, collocation methods
• weeks 8-9. Stiff equations, linear stability theory
• weeks 10-12. Method of lines, IMEX methods, ETD methods, SDC methods
• weeks 13-15. Boundary value problems (shooting methods in 1D, boundary integral methods in 2D)

Course Material: I will post handouts, lecture notes, assignments and asynchronous lectures on bCourses. Please e-mail me (wilkening@berkeley.edu) if you do not have access to the bCourses page.

Grading: 90% Homework, 10% participation (in the form of a 5-7 minute presentation to the class on Zoom)

Homework: 7 assignments (lowest score dropped). Problems will involve a mix of theoretical exercises and programming assignments/mini-projects. I generally find Matlab is the simplest programming language to use for this class, so if you anticipate needing help from Andrew or me on programming assignments, please use Matlab. Assignments will be submitted to Gradescope on selected Fridays by 6 PM Pacific time.