Numerical Simulation-ME210B (cross-listed CS/ECE/ChemE/Math)
Departments of Mechanical Engineering and Computer Science,
Phone: (805)893-5362 (office)
Office: Harold Frank Hall 5107
Office Hours: Mondays 11am-noon and 3-4pm, or email for an appointment
Office Hours: Fridays 9-11am in Harold Frank Hall 5106, or email for an appointment
Development of modern numerical methods for ordinary differential equations including Runge-Kutta and multistep.
Convergence, order and stability analysis. Concepts and capabilities of mathematical software.
- Understanding of fundamental concepts of numerical solution of ODEs, including
sources and propagation of error, and stiffness.
- Experience with practical issues of software development including error control and stepsize selection.
- Capability of applying stability and accuracy concepts from numerical ODEs to numerical PDEs.
- January 7 - Start Homework 1
- January 14 - Homework 1 due, Start Homework 2
- January 21 - UCSB Holiday
- January 23 - Homework 2 due, Start Homework 3
- January 30 - Part 1 of Homework 3 due
- February 4 - Exam 1
- February 11 - Part 2 of Homework 3 due
- February 13 - Start Homework 4
- February 18 - UCSB holiday
- February 20 - Part 1 Homework 4 due, Start Homework 5
- March 4 - Homework 4.II and Homework 5 due, Start Homework 6
- March 13 - Homework 6 due
- March 13 - Exam 2
- February 27 — no class. Both Homework 4 (part 2) and Homework 5 are due on March 4.
- Professor Petzold will be going out of town February 25 immediately after class, so there will be no office hours on that day.
- For the computing homeworks, turn in your SOURCE CODES as well as your results!
- Homeworks may be turned in early to the homework box
- January 30 and February 6 will cover a variable-stepsize derivation of Adams and BDF methods that is
more general than the constant-stepsize derivation in the book. You are responsible for
the variable-stepsize derivation. Here are the notes on that: Notes
- Professor Petzold has moved her Monday office hours from 4pm to 3pm.
- TA's office hours on February 8th are 09:00am-10:00am and 02:15pm-03:15pm.This time, the location is CS Department's Graduate Student Lab (GSL).
- Professor Petzold's office hours on Monday, February 11 are 3-5pm.
Handouts and Other Information:
Lecture Topics and Approximate Schedule (subject to change):
- 1: Standard Form, Existence/Uniqueness Theorem (Section 1.1), Method of Lines (Scholarpedia article), Problem Stability (Section 2.1)
- 2: Stability for Linear Constant-Coefficient and Nonlinear systems (Sections 2.2 and 2.4), Forward Euler Method (Section 3.1)
- 3: Convergence, Accuracy, Consistency (Section 3.2)
- 4: Absolute Stability (Section 3.3), Stiffness (Section 3.4)
- 5: Backward Euler, Functional Iteration, Newton's method (Section 3.4)
- 6: A-stability, stiff decay (Section 3.5), trapezoidal method (Section 3.6), midpoint method, discontinuities (Section 3.7)
- 7: Review, Intro to Higher-Order Methods, Newton form of the Interpolating Polynomial (p. 125)
- 8: Exam 1
- 9: Exam 1 solutions, Multi-step methods: derivation of variable-stepsize Adams (Section 5.1.1, plus extra material)
- 10: Derivation of variable-stepsize BDF methods (Section 5.1.2, plus extra material), Error of variable-stepsize methods
- 11: Implementation of Linear Multistep Methods (Sections 5.4 and 5.5)
- 12: Order, 0-stability and absolute stability for Linear Multistep Methods (Sections 5.2 and 5.3)
- 13: Intro to Runge-Kutta methods (Sections 4.0-4.2)
- 14: Convergence, 0-stability, order (4.3), and absolute stability for Runge-Kutta methods (Section 4.3)
- 15: Error Estimation and stepsize control for Runge-Kutta methods (Section 4.5, omitting the Step Doubling subsection)
- 16: Implicit Runge-Kutta methods (Section 4.7)
- 17: Review
- 18: Exam 2
Linda R. Petzold