Numerical Methods for Differential Equations

MATH 4820 @ RPI

Numerical Methods for Differential Equations

About

Notes and files from MATH4820 in Spring 2020 at RPI.

Instructor: D.W. Schwendeman
Course homepage: link

Notes

Lecture 01, Jan 13: notes - Brief Introduction to First-order ODEs and Higher-order ODEs
Lecture 02, Jan 16: notes - IVPs and BVPs; Well-posed Problems; Lipschitz Condition
Lecture 03, Jan 23: notes - Problem Stability; Single-step Methods
Lecture 04, Jan 27: notes - Single-step Methods; Consistency, Convergence, and Stability
Lecture 05, Jan 30: notes - Runge-Kutta Methods; Absolute Stability
Lecture 06, Feb 03: notes - Absolute Stability
Lecture 07, Feb 06: notes - Stiff Equations and Implicit Methods; Error Control and Step Size Selection
Lecture 08, Feb 10: notes - Multi-step Methods and Its Implementation
Lecture 09, Feb 13: notes - Multi-step Methods; Order of Accuracy and Stability
Lecture 10, Feb 18: notes - Exam 1 Review; Stability for Multi-step Method
Lecture 11, Feb 24: notes - Absolute Stability for Multi-step Methods; Predictor-Corrector Methods
Lecture 12, Feb 27: notes - Boundary Value Problems; Numerical Methods Based on Shooting
Lecture 13, Mar 02: N/A
Lecture 14, Mar 05: notes - Shooting Methods; Finite Difference Methods for BVPs
Lecture 15, Mar 23: notes - Finite Difference Methods; Linear BVPs
Lecture 16, Mar 26: notes - Error Analysis; Non-linear Methods
Lecture 17, Mar 30: notes - Extensions of BVPs
Lecture 18, Apr 03: notes - Numerical Methods for PDEs; Finite Difference Approximations
Lecture 19, Apr 06: notes - Analysis of Error; Stability
Lecture 20, Apr 13: notes - Stability; Fourier Stability Analysis
Lecture 21, Apr 16: notes - Implicit Methods for Heat Equations; Extensions; Wave Equations
Lecture 22, Apr 20: notes - Wave Eqn - Problem Stability and Energy Estimation; Numerical Methods; Higher-Order Accurate Scheme

Homework

Exams

Last Updated: Apr 27