A CNN Based Approach for Solving a Hyperbolic PDE Arising from a System of Conservation Laws - the Case of the Overhead Crane

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• 作者：Daniela Danciu (19)
  
• 关键词：CNN ; method of lines ; hyperbolic PDE ; ODE ; conservation laws ; neurocomputing ; neuromathematics ; Courant ; Isaacson ; Rees rule
• 刊名：Lecture Notes in Computer Science
• 出版年：2013
• 出版时间：2013
• 年：2013
• 卷：7903
• 期：1
• 页码：375-385
• 全文大小：481KB
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• 作者单位：Daniela Danciu (19)
  
  19. Department of Automatic Control, University of Craiova, 13, A.I. Cuza str., 200585, Craiova, Romania
  
• ISSN：1611-3349

文摘

The paper proposes a neurocomputing approach for numerical solving of a hyperbolic partial differential equation (PDE) arising from a system of conservation laws. The main idea is to combine the method of lines (transforming the mixed initial boundary value problem for PDE into a high dimensional system of ordinary differential equations (ODEs)) with a cellular neural network (CNN) optimal structure which exploits the inherent parallelism of the new problem in order to reduce the computational effort and storage. The method ensure from the beginning the convergence of the approximation and preserve the stability of the initial problem.