Math 593 Numerical Methods in PDEs

Spring 2020

 

Instructor: Baver Okutmuştur       Office: M242                  Tel: 210 2974                          email: baver@metu.edu.tr

Lectures: Tuesday  10:40-13:30  M205

 

Exams and Grading:

 

                                     Midterm (30%) TBA
                                     Homework (30%)
                                     Final (40%) (TBA)

 

Make-up Exam : No Make-up examination will be offered

 

Course webpage : http://users.metu.edu.tr/baver/593.htm

 

Purpose: of the course: 

·         To apply the  numerical techniques for the solutions of parabolic, elliptic and hyperbolic partial differential equations

·         To identify, formulate, and solve the partial differential equations numerically

·         Provide the knowledge on the finite difference technique and its application

·         To understand the convergence, consistency, stability of the numerical techniques

·         To analyze the truncation error and its order

 

Content:

 

 

  1. Essential preliminaries.
  2. Finite difference method, stability, convergence and error analysis.
  3. Initial and boundary conditions, irregular boundaries.
  4. Parabolic equations; explicit and implicit methods, stability analysis, error reduction, variable coefficients, derivative boundary conditions, solution of tridiagonal systems.
  5. Elliptic equations, iterative methods, rate of convergence.
  6. Hyperbolic equations. The Lax-Wendroff method, variable coefficients, systems of conservation laws, stability
  7. Finite volume method.

 

 

Text Book(s) and references:

1.      Numerical Solution of PDEs. Finite Difference Methods. G.D. Smith, Claredon press, Oxford. 3rd edt, 1985.

2.      Numerical Solution of Partial Differential Equations, Gordon Everstine, 2010

3.      Numerical PDE for Environmental Sciences and Engineers, D. R. Lynch, Springer 2005.

4.      Finite Difference Methods for Ordinary and Partial Differential Equations, Randall J. LeVeque, SIAM, 2007.

5.      Numerical Solution of Hyperbolic PDE, J. A. Trangenstein, Cambridge Press, 2007

  1. Jurgen Jost, PDE, Springer 2002
  2. George F. Carrier Carl E. Pearson, PDE, Academic Press 1976

8.      Finite Volume Methods for Hyperbolic Problems, Randall J. LeVeque, Cambridge University Press  2002.