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Classical and new numerical schemes are generated using evolutionarycomputing. Differential Evolution is used to find the coefficients of finitedifference approximations of function derivatives, and of single and multi-stepintegration methods. The coefficients are reverse engineered based on samplesfrom a target function and its derivative used for training. The Runge-Kuttaschemes are trained using the order condition equations. An appealing featureof the evolutionary method is the low number of model parameters. Thepopulation size, termination criterion and number of training points aredetermined in a sensitivity analysis. Computational results show good agreementbetween evolved and analytical coefficients. In particular, a new fifth-orderRunge-Kutta scheme is computed which adheres to the order conditions with a sumof absolute errors of order 10^-14. Execution of the evolved schemes proved theintended orders of accuracy. The outcome of this study is valuable for futuredevelopments in the design of complex numerical methods that are out of reachby conventional means.

Evolutionary Design of Numerical Methods: Generating Finite Difference and Integration Schemes by Differential Evolution