Computational Partial Differential Equations (MATH 5602)

Instructor: Ching-Shan Chou

Classes: MWF 15:00-16:55 at EA295

Pre-requisite: ((Math 4512 or Math 4557) and Math 5601) -OR- ((Math 512 or Math 557) and Math 556 and (Math 568 or Math 572)). Not open to students with credit for Math 606.

Textbook: "Numerical Solutions of Partial Differential Equations: Finite Difference Methods" by G.D. Smith, third edition.

References: (1) MATLAB tutorial: http://www.mathworks.com/academia/student_center/tutorials/launchpad.html

Office Hours: by appointment.

Homework: Assignments are listed below. Homework assigned throughout the week (Mon, Wed, Fri) will be collected on the follwoing Friday. Late Homework will not be accepted.

Grading: (1) Homework 40%, (2) Midterm (in class) 30%, (2) Final Exam (project) 30%. The letter grade will be with an approximately 90(A)-80(B)-70(C)-60(D) scale.

Disability Statement: Students with disabilities that have been certified by the Office for Disability Services will be appropriately accommodated, and should inform the instructor as soon as possible of their needs. The Office for Disability Services is located in 150 Pomerene Hall, 1760 Neil Avenue; telephone (614) 292-3307 and VRS (614) 429-1334; webpage  http://www.ods.ohio-state.edu.

Tentative Class Schedule & Sample Codes
Schedule
Codes
Week 1 Parabolic equations: finite difference, explicit methods and stability  
Week 2 Parabolic equations: Crank-Nicolson method, linear solvers and stability  
Week 3 Parabolic equations: local truncation error, consistency, stability and convergence  
Week 4 Parabolic equations: method of lines  
Week 5 Parabolic equations: stiff problems and nonlinear solvers  
Week 6 Hyperbolic equations: transport equation and shock formation Notes.pdf
Week 7 Hyperbolic equations: upwind, Lax-Friedrichs and Lax-Wendroff methods PracticeExam.pdf
Week 8 Hyperbolic equations: stability analysis of the methods and their convergence Upwind_LF.m
Week 9 Hyperbolic equations: flux limiters and system problems  
Week 10 spring break  
Week 11 Hyperbolic equations: boundary conditions  
Week 12 Elliptic equations: introduction of direct solvers  
Week 13 Elliptic equations: introduction of iterative solvers  
Week 14 Elliptic equations: convergence analysis  
Week 15 Projects  

 

Homework

Due Date
Assigned homework
1/11 no homework due
1/18 (page 79) 1, 2
1/25 homework assigned in class, (page 86) 7
2/1 (page 93) 12, (page 94) 13
2/8 (page 97-99) 18, 19, 20
2/15 no homework
2/22 no homework
3/1 hw8.pdf
3/8  
3/15 spring break
3/22 hw9.pdf
3/29 no homework
4/5 hw11.pdf
4/12  
4/19