Given below is a problem where it is shown that proper modeling is key to solving engineering problems. An improper model and a proper model may lead to opposite conclusions
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Dear Professor Autar Kaw,
I agree with you that not all of mathematics model can be solved exactly in analytical form. In this address :
http://math152.wordpress.com/2008/12/07/the-stochastic-group/#comment-242
there are several first order ODE that require implementation of your numerical schemes.
Hopefully this information useful for all visitors here.
Sincerely yours,
Rohedi.
Physics Dept, Faculty of Natural Sciences,
Sepuluh Nopember Institute of Technology (ITS) Surabaya, Indonesia.