PHY201 - Worksheet 2, F00

Numerical Calculation of erf(x)- Part I

Aleksandar Donev - Dr. Phillip Duxbury

Due Friday September 15th

Physics 201 home

The normal probability distribution function involves integrals of the form $\int_{0}^{x}e^{-t^{2}}dt$. This integral can not be solved in terms of standard transcendental and algebraic functions, so a new special function called the error function is introduced:

$$erf(x)=\frac{2}{\sqrt{\pi }}\int_{0}^{x}e^{-t^{2}}dt$$ (1)

The next few worksheets in this class will use several different ways of evaluating this function to illustrate several of the key features of programming in Fortran 90. We will mainly concentrate on two ways of evaluating equation 1, namely, truncated power series and numerical integration. Notice that the argument of the error function can be a complex number, in which case the integral needs to be done in the complex plane.