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CPS615-Discussion of Ordinary Differential Equations and Start of Parallel N-Body Algorithm
Given by Geoffrey C. Fox at Delivered Lectures of CPS615 Basic Simulation Track for Computational Science on 10 October 96. Foils prepared 28 December 1996
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This discusses solution of systems of ordinary differential equations (ODE) in the context of N squared particle dynamics problems
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We start with motivation with brief discussion of relevant problems
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We go through basic theory of ODE's including Euler, Runge-Kutta, Predictor-Corrector and Multistep Methods
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We begin the discussion of solving N body problems using classic Connection Machine elegant but inefficient algorithm
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Note -- Some foils expanded to two after talk and second one is given without audio in script
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This mixed presentation uses parts of the following base foilsets which can also
be looked at on their own!
CPS615Master96 Master Set of Foils for 1996 Session
of CPS615
CPS615-95E CPS615 Foils -- set E: ODE's and
Particle Dynamics
CPS 615 Lectures 1996 Fall Semester -- October 10
CPS615Master96 067 001 Delivered Lectures for
CPS615 -- Base Course for
the Simulation Track of
Computational Science
Fall Semester 1996 --
Lecture of October 10 - 1996
CPS615Master96 080 002 Abstract of Oct 10 1996
CPS615 Lecture
Introduction to N body Algorithms
CPS615-95E 004 003 Particle Applications -
Ordinary Differential
Equations (ODE's)
CPS615-95E 005 004 Particle Applications - the
N-body problem
CPS615-95E 006 005 Newton's First Law -- The
Gravitational Force on a
Particle
CPS615-95E 007 006 Equations of Motion --
Newton's Second Law
Overview of Numerical Methods for Ordinary Differential Equations
CPS615-95E 008 007 Numerical techniques for
solving ODE's
CPS615-95E 009 008 Second and Higher Order
Equations
CPS615-95E 010 009 Basic Discretization of
Single First Order Equation
CPS615-95E 011 010 Errors in numerical
approximations
CPS615-95E 012 011 Runge-Kutta Methods: Euler's
method
CPS615-95E 013 012 Estimate of Error in Euler's
method
CPS615-95E 014 013 Relationship of Error to
Computation
CPS615-95E 015 014 Example using Euler's method
from the CSEP book
CPS615-95E 016 015 Approximate solutions at
t=1,using Euler's method
with different values of h
CPS615-95E 017 016 Runge-Kutta Methods:
Modified Euler's method
CPS615-95E 018 017 Approximate solutions of the
ODE for et at t=1, using
modified Euler's method with
different values of h
CPS615-95E 019 018 The Classical Runge-Kutta --
In Words
CPS615-95E 020 019 The Classical Runge-Kutta --
Formally
CPS615-95E 021 020 The Classical Runge-Kutta
Pictorially
CPS615-95E 022 021 Predictor / Corrector
Methods
CPS615-95E 023 022 Definition of Multi-step
methods
CPS615-95E 024 023 Features of Multi-Step
Methods
CPS615-95E 025 024 Comparison of Explicit and
Implicit Methods
First Part of N Body Discussion
CPS615-95E 026 025 Solving the N-body equations
of motion
CPS615-95E 027 026 Representing the N-Body
problem
CPS615-95E 028 027 Form of the Computation
CPS615-95E 029 028 N-body Runge Kutta Routine
in Fortran90 - I
CPS615-95E 030 029 Runge Kutta Routine in
Fortran90 - II
CPS615-95E 031 030 Computation of accelerations
- a simple parallel array
algorithm
CPS615-95E 032 031 Simple Data Parallel Version
of N Body Force Computation
-- Grav -- I
CPS615-95E 033 032 The Grav Function in Data
Parallel Algorithm - II
List of Foils Used as they occur
CPS615Master96 Master Set of Foils for 1996 Session
of CPS615
67 80
CPS615-95E CPS615 Foils -- set E: ODE's and
Particle Dynamics
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
Sorted List of Foils Used
CPS615Master96 Master Set of Foils for 1996 Session
of CPS615
67 80
CPS615-95E CPS615 Foils -- set E: ODE's and
Particle Dynamics
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
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