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Original Articles

A hybrid genetic programming approach for the analytical solution of differential equations

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Pages 279-299 | Received 01 Mar 2004, Accepted 16 Dec 2004, Published online: 26 Jan 2007

References

References

  • Banzhaf W Nordin P Keller RE Francone FD Genetic Programming: An Introduction: On the Automatic Evolution of Computer Programs and Its Applications San Francisco Morgan Kaufmann Publishers 1998
  • Burgess G Finding approximate analytic solutions to differential equations using genetic programming Technical Report DSTO-TR-0838 Australia Surveillance Systems Division, Defence Science and Technology Organisation 1999
  • Cao , H , Kang , L , Chen , Y and Yu , J . 2000 . Evolutionary modeling of systems of ordinary differential equations with genetic programming . Genetic Programming & Evolvable Machines , 1 ( 4 ) : 309 – 337 .
  • Chang , CL and Lee , ZY . 2003 . Applying the double side method of weighted residual for solving circle plate large deformation problems . Applied Mathematics and Computation , 141 ( 2–3 ) : 477 – 490 .
  • Chen , CK , Hung , CI and Lee , ZY . 2002 . Double side approach method to obtain solutions for transient nonlinear heat conduction using genetic algorithms . Applied Mathematics and Computation , 133 ( 2–3 ) : 431 – 444 .
  • Diver , DA . 1993 . Applications of genetic algorithms to the solution of ordinary differential equations . Journal of Physics A: Mathematical and General , 26 : 3503 – 3513 .
  • Ikeda , Y . 2003 . Estimation of chaotic ordinary differential equations by coevolutional genetic programming . Electronics and Communications in Japan, Part III: Fundamental Electronic Science , 86 ( 2 ) : 1 – 12 .
  • Koza JR Genetic Programming Cambridge, MA The MIT Press 1992
  • Koza JR Genetic Programming II Cambridge, MA The MIT Press 1994
  • Koza JR Genetic Programming III San Francisco, CA Morgan Kaufmann 1999
  • Mills AF Heat and Mass Transfer Chicago, IL Irwin 1995
  • Myers GE Analytical Methods in Conduction Heat Transfer Schenectady, NY Genium Publishing Corp. 1987
  • Sakamoto , E and Iba , H . 2001 . Inferring a system of differential equations for a gene regulatory network by using genetic programming . Proceedings of the IEEE Conference on Evolutionary Computation , 1 : 720 – 726 .
  • Taylor AE Mann WR Advanced Calculus 3rd ed. New York, NY Wiley 1983
  • Xiong S Wang W Li F A new genetic programming approach in symbolic regression Proceedings of the 15th IEEE International Conference on Tools with Artificial Intelligence 161 165 2003

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