Integration Wavelet Neural Network for Steady Convection Dominated Diffusion Problem
ICIC), 2010 Third International Conference（2010）
摘要
In this paper, we first propose an Integration Wavelet Neural Network (I_WNN) based on spline wavelet functions for solving differential equations. Then the proposed method is verified successfully by solving two steady convection dominated diffusion problems and the numerical perturbation doesn't happen when the ratio of convective coefficient to diffusive coefficient is as high as 100. Moreover, once the I_WNN is trained and the parameters are stored, it allows instantaneous evaluation of solution at any desired point spending negligible computing time and memory and the maximum relative error is 1.13%.
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关键词
wnn,integration wavelet neural network,maximum relative error,convection dominated,integration,wavelet transforms,steady convection dominated diffusion problem,diffusion problem,instantaneous evaluation,diffusive coefficient,instantaneous solution evaluation,differential equation,negligible computing time,spline wavelet function,spline wavelet functions,numerical perturbation,differential equations,splines (mathematics),spline wavelet,neural nets,convective coefficient,steady convection dominated diffusion,least squares approximation,spline,stability,computer networks,relative error,finite element methods,artificial neural networks,neural networks
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