Math-305, Numerical Methods & Matrices
Chapter 6 — Numerical Solutions of ODEs

Dr. Kevin G. TeBeest

 
As always, rework the examples I worked in class before attempting the homework.


This is a running assignment. Work through these problems AS we cover each method.


PROBLEM:  Approximate the solution of the initial value problem (IVP)

y'   =   5 sin(2x)     y ,

y(0)   =   1 ,

from x = 0 to x = 1 with stepsize h = 0.2 using:

  1. Euler's method,

  2. the implicit Euler method,

  3. the trapezoidal method,

  4. the modified Euler (predictor-corrector) method,

  5. the classical Runge-Kutta method. (Compute y1 and y2 only.)

For comparison, from MATH-204 we find that the exact solution of the IVP is

y*(x)   =   ex + sin(2x) 2 cos(2x) .

In each method above, determine the error of the approximation at each node. For example, the error at node n is

En   =   y*(xn) yn .

Here are the ANSWERS you should obtain.


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