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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
Secs 44.6

This discusses solution of systems of ordinary differential equations (ODE) in the context of N squared particle dynamics problems
We start with motivation with brief discussion of relevant problems
We go through basic theory of ODE's including Euler, Runge-Kutta, Predictor-Corrector and Multistep Methods
We begin the discussion of solving N body problems using classic Connection Machine elegant but inefficient algorithm
Note -- Some foils expanded to two after talk and second one is given without audio in script

This mixed presentation uses parts of the following base foilsets which can also be looked at on their own!
Master Set of Foils for 1996 Session of CPS615
CPS615 Foils -- set E: ODE's and Particle Dynamics

Table of Contents for CPS615-Discussion of Ordinary Differential Equations and Start of Parallel N-Body Algorithm

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CPS 615 Lectures 1996 Fall Semester -- October 10
1 Delivered Lectures for CPS615 -- Base Course for the Simulation Track of Computational Science
Fall Semester 1996 --
Lecture of October 10 - 1996
2 Abstract of Oct 10 1996 CPS615 Lecture
Introduction to N body Algorithms
3 Particle Applications - Ordinary Differential Equations (ODE's)
4 Particle Applications - the N-body problem
5 Newton's First Law -- The Gravitational Force on a Particle
6 Equations of Motion -- Newton's Second Law
Overview of Numerical Methods for Ordinary Differential Equations
7 Numerical techniques for solving ODE's
8 Second and Higher Order Equations
9 Basic Discretization of Single First Order Equation
10 Errors in numerical approximations
11 Runge-Kutta Methods: Euler's method
12 Estimate of Error in Euler's method
13 Relationship of Error to Computation
14 Example using Euler's method from the CSEP book
15 Approximate solutions at t=1,using Euler's method with different values of h
16 Runge-Kutta Methods: Modified Euler's method
17 Approximate solutions of the ODE for et at t=1, using modified Euler's method with different values of h
18 The Classical Runge-Kutta -- In Words
19 The Classical Runge-Kutta -- Formally
20 The Classical Runge-Kutta Pictorially
21 Predictor / Corrector Methods
22 Definition of Multi-step methods
23 Features of Multi-Step Methods
24 Comparison of Explicit and Implicit Methods
First Part of N Body Discussion
25 Solving the N-body equations of motion
26 Representing the N-Body problem
27 Form of the Computation
28 N-body Runge Kutta Routine in Fortran90 - I
29 Runge Kutta Routine in Fortran90 - II
30 Computation of accelerations - a simple parallel array algorithm
31 Simple Data Parallel Version of N Body Force Computation -- Grav -- I
32 The Grav Function in Data Parallel Algorithm - II
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