Symbolic Regression for Approximating Analytic Solutions to Differential Equations

Approximate analytic expressions are obtained for initial value problems with purely numerical solutions. Symbolic regression was utilized to obtain such analytic expression. For functions that are Lipschitz continuous, results revealed that the maximum absolute error (sup-norm) is bounded.

symbolic regression, initial value problem, finite difference method

1. Blickle T. and Thiele L. (1994).Genetic programming and redundancy. In J. Hopf, editor, Genetic Algorithms Workshop at KI-94, pages 33–38. Max-Planck-Institut f¨ur Informatik. [Google Scholar] [Crossref]

2. Gelly Sylvain, Teytaud Olivier, Bredeche Nicolas, Schoenauer Marc (2017) Symbolic regression, parsimony, and some theoretical considerations about GP search space .Equipe TAO - INRIA Futurs, LRI, Bat. 490, University Paris-Sud, 91405 Orsay Cedex. France [Google Scholar] [Crossref]

3. Grossmann, C, Hans-G. Roos; Martin Stynes (2007). Numerical Treatment of Partial Differential Equations. Springer Science & Business Media. [Google Scholar] [Crossref]

4. Hoffman JD; Frankel S (2001). Numerical methods for engineers and scientists. CRC Press, Boca Raton. [Google Scholar] [Crossref]

5. Iserlas, A. (2008). A first course in the numerical analysis of differential equations. Cambridge University Press. [Google Scholar] [Crossref]

6. Koza J. R.(1992). Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge, MA, USA. [Google Scholar] [Crossref]

7. Regalado et al. (2019). Approximate Analytic Solution To The Lotka-Volterra Predator–Prey Differential Equations Model. Journal of Higher Education Research Disciplines 4 (1), 38-47. [Google Scholar] [Crossref]

8. Strikwerda, J/ (2004). Finite Difference Schemes and Partial Differential Equations (2nd ed.). SIAM. [Google Scholar] [Crossref]

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