Numerical calculations are just a part of the way we do science now. It isn't cheating, it's a legitimate method. If the results of the numerical calculation agree with actual data, then it works.

Shuiping Yang, Aiguo Xiao, AN EFFICIENT NUMERICAL METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH TWO CAPUTO DERIVATIVES, Journal of Computational Mathematics, Vol. 34, No. 2 (March 2016), pp.

Scientists developed a method combining effective theory and duality transformations to simplify and solve complex quantum systems with strong interactions.

The paper deals with a numerical method for solving nonlinear integro-parabolic problems of Fredholm type. A monotone iterative method, based on the method of upper and lower solutions, is constructed ...

A research team led by TU Darmstadt has transformed a difficult problem in quantum physics into a much simpler version through innovative reformulation – without losing any important information. The ...