College Physics ›› 2020, Vol. 39 ›› Issue (03): 72-77.

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The difference method forsolving the reaction-diffusion equation —Planetary cooling model as an example

WU Jin-tai,LI Jin-da,JIANG Si-yi,LEI Lei,LI Xiang-hua   

  1. Department of Astronomy,School of Physics and Astronomy,Yunan University,Kunming 650504,China
  • Received:2019-07-19 Revised:2019-11-28 Online:2020-03-20 Published:2020-03-14


The reaction-diffusion equation is a kind of non-linear parabolic equation,which has been widely used in many physical models. An earth-like planetary cooling model is considered in this paper.Through reasonably assuming the heat conduction characteristics of each layer inside the planet,a set of reaction-diffusion equation is

  constructed.Also,different boundary conditions and initial conditions are deduced according to the actual physical

  situation.Then,based on the idea of finite difference method,the equations could be solved numerically by comput

  er programs.Finally,the variation of temperature distribution inside the planet with time is shown.

Key words: reaction-diffusion equation, earth-like planet, heat conduction, finite difference method