This course is no longer offered

20366 Numerical Methods for Ordinary Differential Equations

Credits: 3 advanced credits 1 in Mathematics or in Computer Science

Prerequisites: Students must fulfill all English requirements and take bibliographic instruction in the Library.

Required: Infinitesimal Calculus I, Infinitesimal Calculus II, Linear Algebra I, Ordinary Differential Equations I,2 Numerical Analysis,3 as well as having accumulated at least 30 credits in Mathematics

The course, based on “Numerical methods for ordinary differential equations,” part of An Introduction to Numerical Analysis, by K.E. Atkinson (John Wiley & Sons, 1978), was developed by Judith Gal-Ezer and Igal Kasas.

Numerical solution of ordinary differential equations is one of the cornerstones of numerical analysis; it is of interest to students of Mathematics and Computer Science as well as to students of Engineering and the Natural Sciences with sufficient background. The course deals with the numerical solution of initial value problems, presenting various solution methods. It provides motivations and mathematical justifications of these methods, and deals with convergence analysis, truncation errors and stability. The theoretical discussion is followed by actual implementation of the solution methods – writing and running computer programs.

Topics: A one-step method – Euler’s method; Multistep methods – the midpoint method, the trapezoidal method, predictor-corrector methods, the Adams-Bashforth and Adams-Moulton methods; the Runge-Kutta methods.

1Students studying toward a degree in Mathematics or Computer Science, please note: the credits for this course will be considered credits in Mathematics or in Computer Science, as necessary.

2Students who took Introduction to Differential Equations (20218) are advised to contact a Mathematics advisor for instructions on how to acquire the necessary background by themselves.

3or Numerical Computation (20233), which is no longer offered.