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This work establishes the existence of addition theorems and double-angleformulas for Ck real scalar functions. Moreover, we determine necessary andsufficient conditions for a bivariate function to be an addition formula for aCk real function. The double-angle formulas allow us to generate a duplicationalgorithm, which can be used as an alternative to the classical numericalmethods to obtain an approximation for the solution of an ordinary differentialequation. We demonstrate that this algorithm converges uniformly in any compactdomain contained in the maximal domain of that solution. Finally, we carry outsome numerical simulations showing a good performance of the duplicationalgorithm when compared with standard numerical methods

Addition theorems for Ck real functions and applications in ordinary differential equations