Math 224-01: Differential Equations: Reading Homework 2.6

1. Computer Implementation :
   
   1. Using Numerical Solvers : how is a solver likely to calculate the step-size to use in solving a differential equation? how is this related to what the user specifies?
      
   2. Solver Errors : what different types of error are there in a numerical calculation? what are the problems with using a step-size that is too large or too small?
      
   3. Step-Size Errors : what errors are illustrated in examples 2.6.1 and 2.6.2? how is this different than in 2.6.3?