Many problems in physics are described by differential equations. This is due in part to the basic laws of nature (like Newton's second and Schrödinger equation) being differential in form,
![[Newton eqn]](img2a.gif){kind=small}
![[Schroedinger eqn]](img2b.gif){kind=small}
The differential nature of these physical laws in turn may be a reflection of our use of continuous variables like position and probability. (The use of differential equations may also reflect traditionally-trained physicists viewing problems in differential forms.) A differential equation can be transformed into an integral equation, but since integral equations are not how we usually learn physics, laws are hardly ever stated originally as integral equations. This may change in the future as computational techniques make integral equations straightforward to solve. See a later Chapter.
The project in this chapter is formulated with differential equations.
More specifically the the physical problem is:
a non relativistic particle with mass m
moves in one dimension under
the influence of a conservative force F in
an inertial frame of reference.
We want to obtain the displacement x(t), the velocity
and the acceleration 
as functions of time.
At the begining we will solve the linear oscillator
![[oscillator eqn]](img5.gif){kind=small}
and later the anharmonic
The model consists in using discrete methods to solve differential equations.
The method consists of numerical techniques for the integration of differential equations.
The implementation is achieved with a program in C language (you can use another language like FORTRAN or Pascal, or programs like Maple or Mathematica).
An investigation is proposed for further work on the topic.
The methodology and objectives of this project were designed according to the (UCES) paradigm.
Before starting with the solution of the differential equation for the oscillator, some semantics are introduced.
Author:
Rubin H. Landau
For more information e-mail:
rubin@physics.orst.edu
Coauthor: Manuel J. Páez, mpaez@graphy.physics.orst.edu