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Study and application of optimization algorithm about nonlinear partial differential equations with boundary value problem

Liu Tie-Lin Hou Xiang-Lin Zhai Zhong-Hai

Study and application of optimization algorithm about nonlinear partial differential equations with boundary value problem

Liu Tie-Lin, Hou Xiang-Lin, Zhai Zhong-Hai
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  • PDF Downloads:  1023
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Publishing process
  • Received Date:  02 October 2010
  • Accepted Date:  22 December 2010
  • Published Online:  15 September 2011

Study and application of optimization algorithm about nonlinear partial differential equations with boundary value problem

  • 1. (1)School of Civil Engineering, Shenyang Jianzhu University, Shenyang 110168, China; (2)School of Science, Shenyang Jianzhu University, Shenyang 110168, China

Abstract: For elliptic nonlinear partial differential equations with boundary value problem, based on difference method and dynamic design variable optimization method, by taking unknown function value on discrete net point as design variables, difference equation of all the discrete net points is constructed as an objective function. A kind of optimization algorithm about solving unknown function value on discrete net point is proposed. Universal computing program is designed. Practical example is analyzed. By comparing the computing result with the analytical solution, effectiveness and feasibility are verified. Thus complicated nonlinear mathematical physics equations can be solved by the numerical calculation method.

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