Numerical solution of Helmholtz equation by the modified Hopfield finite difference techniques Export

@article{Nourian_08, abstract = {One property of the Hopfield neural networks is the monotone minimization of energy as time proceeds. In this article, this property is applied to minimize the energy functions obtained by finite difference techniques of the Helmholtz-equation. The mathematical representation and correlation between finite difference techniques and modified Hopfield neural networks of the Helmholtz equation are presented. Significant advantages of the above method are its parallel, robust, easy programming nature, and ability of direct hardware implementation. Results of numerical simulations are described and analyzed to demonstrate the method. The results obtained using the proposed method show a very good agreement with theoretical and numerical solutions. {\copyright} 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008}, address = {Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran 15914, Iran; Department of Electrical Engineering, Amirkabir University of Technology, Tehran 15914, Iran}, author = {Dehghan, Mehdi and Nourian, Mojtaba and Menhaj, Mohammad B.}, citeulike-article-id = {3353101}, citeulike-linkout-0 = {http://dx.doi.org/10.1002/num.20366}, citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/121358365/ABSTRACT}, doi = {10.1002/num.20366}, journal = {Numerical Methods for Partial Differential Equations}, keywords = {artificial\_neural\_networks, hopfield\_neural\_networks, ode\_pde\_numerical}, number = {9999}, pages = {NA+}, posted-at = {2008-09-29 17:35:15}, priority = {2}, title = {Numerical solution of Helmholtz equation by the modified Hopfield finite difference techniques}, url = {http://dx.doi.org/10.1002/num.20366}, volume = {9999}, year = {2008} }

TY - JOUR ID - Nourian_08 L3 - citeulike-article-id:3353101 N2 - One property of the Hopfield neural networks is the monotone minimization of energy as time proceeds. In this article, this property is applied to minimize the energy functions obtained by finite difference techniques of the Helmholtz-equation. The mathematical representation and correlation between finite difference techniques and modified Hopfield neural networks of the Helmholtz equation are presented. Significant advantages of the above method are its parallel, robust, easy programming nature, and ability of direct hardware implementation. Results of numerical simulations are described and analyzed to demonstrate the method. The results obtained using the proposed method show a very good agreement with theoretical and numerical solutions. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 IS - 9999 JF - Numerical Methods for Partial Differential Equations AD - Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran 15914, Iran; Department of Electrical Engineering, Amirkabir University of Technology, Tehran 15914, Iran TI - Numerical solution of Helmholtz equation by the modified Hopfield finite difference techniques VL - 9999 SP - NA KW - artificial_neural_networks KW - hopfield_neural_networks KW - ode_pde_numerical AU - Dehghan, Mehdi AU - Nourian, Mojtaba AU - Menhaj, Mohammad PY - 2008/// UR - http://dx.doi.org/10.1002/num.20366 ER -