Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (1): 245-257.

• Articles • Previous Articles     Next Articles

Solving the Semilinear Heat Equation with Integral Boundary Conditions in the Reproducing Kernel Space

DU Juan, CUI Ming-Gen   

  1. 1.Department of Mathematics, Harbin Institute of Technology, Shandong Weihai 264209|2.School of Mathematics and Sciences, Harbin Normal University, Harbin 150025
  • Received:2008-07-23 Revised:2009-10-14 Online:2010-01-01 Published:2010-01-01
  • Supported by:

    黑龙江省自然科学基金(A2007-11)和黑龙江省教育厅科学技术研究项目(11541098)资助

Abstract:

In this paper, we give a new method to solve the semilinear heat equation with integral boundary conditions. Its
exact solution is represented in the form of series in the reproducing kernel space. The n-term approximation un(x, t) of the exact solution u(x, t) is proved to converge to the exact solution. Some numerical examples are displayed to demonstrate the accuracy of
the present method.

Key words: Semilinear heat equation, Integral boundary condition, Reproducing kernel space

CLC Number: 

  • 34K10
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