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JVM Instructions 1

In this chapter we do our first simple simulations and introduce some basic numerical methods techniques involving the solution of ordinary differential equations. Such equations are common in physics and here we look a some simple examples that deal with the motion of a mass in a gravitational field and a mass attached to a spring.

Thus far we presented only the basic syntax of the language, so we will carry out the computations in a purely procedural programming manner. That is, we will put all the code within the main() method of an application (or the init() method of an applet) and not use any methods or any object oriented features of the language.

For similar reasons, we will only use console output here and not employ any other I/O or graphics techniques until we cover those topics in later chapters.

The topics here include:

• A brief review of Ordinary Differential Equations
  
• Euler Method for solving ODE
  
• Demonstration program using Euler to solve for the motion of an object falling in a constant gravitational field
  
• Predictor-Corrector method that improves on the Euler method
  
• Demonstration of the predictor-corrector method for solving the motion of a mass attached to a spring.
  
• Exercises

The demo programs will also illustrate some of the floating point issues like round-off errors that we briefly discussed in the Chapter 1: Tech section.

Latest update: Dec.12.2003

            Tech
Arithmetic Ops
Math Class
More on Integers
FP : Overview
FP : Java  
  Demo 1
More Mix/Cast
  Demo 2
Exercises

           Physics
Differential Eq.
Euler Method
  Demo 1
Predictor-Corrector
  Demo 2
Exercises