Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
Introduction
Linear Multistep Methods, General Discussion
Linear Multistep Methods, Tools and Development
Linear Multistep Methods: Issues
Numerical Solutions to Dierential Equations
Lecture Notes #6 Linear Multistep Methods
Peter Blomgren
blomgren.peter@
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
Intermission: Example Time!
The Lorenz System
Numerical Solutions to Dierential Equations
Lecture Notes #8 Example: The Lorenz System
Peter Blomgren,
blomgren.peter@gmail.com
Department of Mathematics and Statistics
Dynamical Systems Group
Computational S
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
Variable Order PredictorCorrector Methods
Numerical Results
Looking Forward
Numerical Solutions to Dierential Equations
Lecture Notes #15 Example: Variable Order LMM Schemes
Peter Blomgren,
blomgren.peter@gmail.com
Department of Mathematics and Statistic
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
Numerical Solutions to Dierential Equations
Lecture Notes #14
Adaptive RKF45 Solver
Peter Blomgren,
blomgren.peter@gmail.com
Department of Mathematics and Statistics
Dynamical Systems Group
Computational Sciences Research Center
San Diego State University
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
Introduction
PredictorCorrector Methods
PredictorCorrector Methods, ctd.
Numerical Solutions to Dierential Equations
Lecture Notes #9 PredictorCorrector Methods
Peter Blomgren,
blomgren.peter@gmail.com
Department of Mathematics and Statistics
Dynamical
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
The Van der Pol Oscillator
Return to Physics Circuit Analysis
The Van der Pol Oscillator, again.
Numerical Solutions to Dierential Equations
Lecture Notes #13
The Van der Pol Oscillator
Peter Blomgren,
blomgren.peter@gmail.com
Department of Mathematics an
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
Introduction
Approximations of e x
Implicit RKMethods for Sti Problems
Numerical Solutions to Dierential Equations
Lecture Notes #11 RungeKutta Methods for Sti ODEs
Peter Blomgren,
blomgren.peter@gmail.com
Department of Mathematics and Statistics
Dynami
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
Recap: Last Lecture
Finding Stability Regions
RungeKutta Methods
Numerical Solutions to Dierential Equations
Lecture Notes #4 Stability Regions Revisited &
RungeKutta Methods
Peter Blomgren,
blomgren.peter@gmail.com
Department of Mathematics and Statist
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
Linear Multistep Methods & Stiness
LMMs & Stiness, ctd.
Initial Value Problems (pass #1) Wrapup
Numerical Solutions to Dierential Equations
Lecture Notes #12
Linear Multistep Methods for Sti Systems
Peter Blomgren,
blomgren.peter@gmail.com
Department of
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
Sti ODEs and Multiscale Phenomena
Dealing with Stiness
Numerical Solutions to Dierential Equations
Lecture Notes #10 Sti ODEs Multiscale Phenomena
Peter Blomgren,
blomgren.peter@gmail.com
Department of Mathematics and Statistics
Dynamical Systems Group
Co
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
The Professor
The Class Overview
The Class.
Introductionary Ramblings.
Numerical Computations
Numerical Solutions to Dierential Equations
Lecture Notes #1 Introduction
Peter Blomgren,
blomgren.peter@gmail.com
Department of Mathematics and Statistics
Dynam
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
Introduction and Recap
Limitations on Achievable Order
Stability Theory
Numerical Solutions to Dierential Equations
Lecture Notes #7 Linear Multistep Methods
Peter Blomgren,
blomgren.peter@gmail.com
Department of Mathematics and Statistics
Dynamical Syste
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
Examples, and Recap
RungeKutta: Outstanding Issues
A Brief History, and RKConstruction Methods
Rooted Trees
Stability of Explicit RungeKutta Methods
Numerical Solutions to Dierential Equations
Lecture Notes #5 RungeKutta Methods, Modern Approach
Peter
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
Calculus Review
Math 541 Review
Numerical Solutions to Dierential Equations
Lecture Notes #2 Calculus and Math 541 Review
Peter Blomgren,
blomgren.peter@gmail.com
Department of Mathematics and Statistics
Dynamical Systems Group
Computational Sciences Rese
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
Eulers Method
Improving Eulers Method
Numerical Solutions to Dierential Equations
Lecture Notes #3 Eulers Method
Peter Blomgren,
blomgren.peter@gmail.com
Department of Mathematics and Statistics
Dynamical Systems Group
Computational Sciences Research Cent
Numerical Solutions to Ordinary Differential Equations
MATH 542

Spring 2013
i left you alone that night
with a bottle in hand
you turned the lights of as i walked into the night
i stood alone on the sidewalk
i took a breath for the last time
thought about you and our life time
i took my pride away
no
i will never let you go
i