Description

Numerical solution of initial value problems for ordinary differential equations by single and multi-step methods; finite-difference methods for two-point boundary value problems; numerical solution of time-dependent partial differential equations by finite-difference and finite-volume methods, with stability, accuracy, and convergence theory; introduction to spectral methods and finite-element methods.

Prerequisites

Permission of the instructor. Comfort and familiarity with undergraduate numerical analysis, ordinary and partial differential equations, and fluency in Python, Matlab, or a similar programming language is expected.

Recommended Texts

• Leveque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM 2007
• Adler, De Sterck, MacLachlan, and Olson, Numerical Partial Differential Equations, SIAM 2025
• Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press 2012