MATH 107 Numerical Differential Equations (4)
Lecture: MWF 1200-1250
Corequisite: Mathematics 107L if offered.
Prerequisites: Mathematics 105A-B; some acquaintance with computer
programming.
Textbook: Richard L. Burden and J. Doublas Faires - NUMERICAL ANALYSIS; 8th Edition.
We will go over Chapters 5, 11 and 12 in this quarter. More references might be posted online.
Midterm : 5/7 in class.
Final : 6/11.
Teaching Assistant: MITCHELL RUEY KHONG
Email: mkhong (at) math.uci.edu
There will be 8 homework assignments consisting of both theorectical
and computational problems. You will find the homework
problems, with their corresponding deadlines, in the course homepage.
No late homework will be collected.
There will be one midterm exam and one final exam. No makeup exam will be given.
Your grade will be determined according to 30% homework,
25% midterm and 45% final. The lowest HW score will be dropped.
Schedule of Lectures (Tentative)
Initial value problems for ordinary differential equations (ODE): 12 lectures
Euler methods
Runge-Kutta methods (RK)
Multistep methods
Higher-Order equations and system of differential equations
Stability
Stiffness
Boundary value problems for ordinary differential equations (ODE): 7 lectures
Shooting method
Finite Difference methods (FDM)
Rayleigh-Ritz method
Numerical solutions to partial differential equations (PDE): 10 lectures
Elliptic PDE
Parabolic PDE
Hyperbolic PDE
Finite element method (FEM)
Lecture 01 (4/02/07 M) : Overview. Discretization. Numerical
differentiations (review)
Reading:
Lecture 02 (4/04/07 W) : Forward Euler method, Backward
Euler method and Trapezoidal method.
Reading: Chapter 4.1 and Chapter 5.1
Lecture 03 (4/06/07 F) : Local truncation error
and Global error analysis.
Reading: Chapter 5.2 and Chapter 5.3
Lecture 04 (4/09/07 M) : Global error analysis.
Taylor methods.
Reading: Chapter 5.2 and Chapter 5.3
Lecture 05 (4/11/07 W) : Taylor methods. Runge-Kutta methods.
Reading: Chapter 5.3 and Chapter 5.4
Lecture 06 (4/13/07 F) : Runge-Kutta methods.
Reading: Chapter 5.4
Lecture 07 (4/16/07 M) : Multisteps methods.
Reading: Chapter 5.6
Lecture 08 (4/18/07 W) : Multisteps methods.
System of ODEs and Higher order ODEs.
Reading: Chapter 5.6 and Chapter 5.9
Lecture 09 (4/20/07 F) : Stability.
Reading: Chapter 5.10
Lecture 10 (4/23/07 M) : Stability. Stiffness.
Reading: Chapter 5.10 and Chapter 5.11
Lecture 11 (4/25/07 W) : Stiffness.
Reading: Chapter 5.11
Lecture 12 (4/27/07 F) : Numerical Rate of Convergence.
Reading:
Lecture 13 (4/30/07 M) : Shooting method for Linear BVP
and Nonlinear BVP.
Reading: Chapter 11.1 and Chapter 11.2
Lecture 14 (5/02/07 W) : Finite difference method for Linear BVP.
Reading: Chapter 11.3.
Lecture 15 (5/04/07 F) : Finite difference method for Linear BVP.
Midterm Review.
Reading: Chapter 11.3 and Chapter 5
Lecture 16 (5/07/07 M) : Midterm
Lecture 17 (5/09/07 W) : Midterm solution. Finite difference
method for Nonlinear BVP.
Reading: Chapter 11.4
Lecture 18 (5/11/07 F) : Rayleigh-Ritz method.
Reading: Chapter 11.5
Lecture 19 (5/14/07 M) : Rayleigh-Ritz method.
Reading: Chapter 11.5
Lecture 20 (5/16/07 W) : Rayleigh-Ritz method.
Reading: Chapter 11.5
Lecture 21 (5/18/07 F) : Finite difference method for
Elliptic PDE
Reading: Chapter 12.1
Lecture 22 (5/21/07 M) : Finite difference method for
Elliptic PDE
Reading: Chapter 12.1
Lecture 23 (5/23/07 W) : Finite difference method for
Parabolic PDE
Reading: Chapter 12.2
Lecture 24 (5/25/07 F) : Finite difference method for
Parabolic PDE
Reading: Chapter 12.2
Lecture 25 (5/30/07 W) : Alternating Direction Explicit (ADE).
Higher dimensional Parabolic equation. Alternating Direction Implicit (ADI).
Reading:
Lecture 26 (6/01/07 F) : General treatment for curved boundary.
Finite difference method for Hyperbolic PDE.
Reading: Chapter 12.3
Lecture 27 (6/04/07 M) : Finite element method.
Reading: Chapter 12.4
Lecture 28 (6/06/07 W) : First order hyperbolic PDE.
Reading:
Lecture 29 (6/08/07 F) : Review for the final.
Reading: