### Courses

##### Last Updated:
29/11/2019 - 15:23

## IAM562 - Introduction to Scientific Computing II

Credit: 3(3-0); ECTS: 8.0
Instructor(s): Önder Türk
Prerequisites: Consent of Instructor(s)

#### Course Catalogue Description

Ordinary Differential Equations: Euler’s method, multistep methods, Runge-Kutta methods, stiff equations, adaptivity; Boundary Value Problems: shooting, collocation, Galerkin; Partial Differential Equations: parabolic, hyperbolic, and elliptic equations; Iterative Methods for Sparse Linear Systems: splitting methods.

#### Course Objectives

This is a course on scientific computing for ordinary differential equations (ODEs) and partial differential equations (PDEs). It includes the construction, analysis and application of numerical methods for ODEs/PDEs. Objects of this course are:

• to motivate the need for efficient numerical methods for solving differential equations
• to understand basic finite difference methods for partial differential equations
• to analyze consistency, stability, and convergence of the finite difference methods
• to solve system of linear equations numerically using direct and iterative methods
• to implement numerical methods on the computer to solve partial differential equations arising from the sciences and engineering.

#### Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

• understand mathematics-numeric interaction, and how to match numerical method to mathematical properties
• make a good choice of methods for a particular ODE problem
• construct appropriate finite-difference approximations to PDEs
• analyze consistency, stability, and accuracy of a finite difference method
• write programs to solve ODEs/PDEs by finite difference methods
• solve challenging problems that are either purely mathematical or practical from various disciplines.

#### Tentative (Weekly) Outline

1. Introduction to ODEs
2. Euler’s Method
3. Multistep Methods for ODEs
4. Runge-Kutta Methods for ODEs
5. Linear Stability Domain
6. Stiff Equations and Adaptivity in Time
7. Boundary Value Problems: shooting, collocation, Galerkin
8. Introduction to PDEs
9. Parabolic Equations
10. Parabolic Equations: stability
11. Hyperbolic Equations
12. Elliptic Equations
13. PDEs in Cylindrical and Spherical Coordinates
14. Iterative Solvers: splitting methods

#### Course Textbook(s)

• A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, 2009.
• R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady- State and Time-Dependent Problems, SIAM, 2007.

#### Supplementary Materials and Resources

• Books:
• M. T. Heat, Scientific Computing, McGraw Hill, 1997.
• A. Quarterioni, R. Sacco, and F. Salari, Numerical Mathematics, Springer, 2000.
• A. Quarterioni and F. Salari, Scientific Computing with MATLAB and Octave, Springer-Verlag, 2006.
• David F. Griffiths, John W. Dold, David J. Silvester, Essential Partial Differential Equations: Analytical and Computational Aspects, Springer, 2015.
• Resources:
• MATLAB
• htps://odtuclass.metu.edu.tr