Numerical Methods for Partial Differential Equations

Course Description

Finite difference methods for solving initial value problems of partial differential. Parabolic equations: explicit finite difference approximation, Crank Nicolson implicit method. Fundamental concepts of consistency, accuracy, stability and convergence of finite difference methods. Hyperbolic equations and characteristics. Elliptic equations.

Course Objectives & Outcomes
Objectives:

• Equip the student with necessary knowledge and skills to enable him to discuss the finite differences method applied to partial differential equations. 
•  Develop skills in applying the finite differences method to various partial differential equations.
•  Develop skills in analyzing consistency, accuracy, stability and convergence of finite difference methods. 
• Enable the student to implement numerical solution algorithms applied to the finite differences method for solving different partial differential equations.

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

• Define fundamental concepts of consistency, accuracy, stability and convergence,
•  Describe appropriate solution procedures for a given partial differential equation, 
• Apply finite difference schemes for given partial differential equations,
•  Discuss some theoretical results for the finite differences method,
• Solve a system of partial differential equations by the finite differences method in a modern computer language

References
1. Thomas, J.W. (1995) Numerical Partial Differential Equation: Finite differences method, Springer, ISBN: 978-1-4419-3105-4, e-ISBN: 978-1-4899-7278-1.
 2. Evans, G., Blackledge, J., Yardley, P. (2001) Numerical Methods for Partial Differential Equations, Springer. ISBN 978-1-4471-0377-6.
 3. Smith, G.D. (1985) Numerical Solution for Partial Differential Equations, 3rd edition, Oxford University Press. ISBN 0-19-859650-2.

Course ID: MATH 509