Beware of errors in numerical problem-solving understand how to detect and prevent common errors when using mathematical software tools.

Three potential causes of errors caused by the use of mathematical software packages such as Excel, Matlab and Polymath, and the solutions to prevent them are discussed. The first cause of the error is that no consideration is given to problem parameter uncertainties so the sensitivity analysis is carried out to rectify the errors. The analysis is applied only to physical quantities obtained as the final results of computation. Another cause of error is the use of inappropriate statistics and graphical representations to analyze regression models that can be detected by analyzing a residual plot that is a proper graphical means to test the goodness of fit between a regression model and the data. Lastly, the careless rounding of model parameters is an error that occurs when copying or pasting data in the databases, documents and programs. Proper attention to the potential causes of errors can considerably improve the reliability of the results of numerical problem solving and in the correlation of data.