Introduction
Essentials
Structure
Keywords
Primitive Types
Comments
Literals
Expressions
Operators
Statements
Casts & Mixing
Strings
Console Output 
   Demo
Exercises

    Supplements
Conditional: if-else
Repetitions
Flow Control
Java vs C/C++
JVM Instructions 1

The Euler method uses the derivative at one point to extrapolate to the value at the next point. If the derivative, in fact, varies significantly over that range, the extrapolated point may also differ significantly from the true value.

There are a number methods more sophisticated methods than the Euler approach to reduce these discrepancies.

We will discuss the first order Predictor-Corrector method here, which is slightly more reliable than the Euler method, and in later chapters discuss some more powerful higher order methods.

The Predictor-Corrector improves on the Euler method, by first estimating, or predicting, the next value using the Euler approach:

        Predictor formula

Then this value x_p value helps to obtain an improved value:

       Corrector formula

We see that the corrector uses the average of the derivatives at the old position and at the predicted position to get a better estimate of the next value.

This demonstration program uses the Predictor-Corrector method to obtain the position and velocity of a mass attached to a spring.

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