ERROR FUNCTIONS COMMONLY OCCUR IN GROUND WATER FLOW AND TRANSPORT SOLUTIONS

Simply calculate the value within the brackets as beta, then find that value in the table and substitute it for the entire term (erf[beta]), just as you would if you were taking a log or a sin. The complimentary error function is 1-erf. Be careful if you get a negative value for beta because a negative beta yields -erf(beta) and if you are seeking a complimentary error function, this will be 1-(-erf(beta).

If you need an expression to estimate an error function, it can be approximated using the following two expressions:



and:



However I find that linear interpolation within the table is more accurate for values between -3 and +3. The full error function is shown below with a table of values: