فهرست مقالات Nonlinear ‎ODE‎

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  1 - Solving Volterra's Population Model via Rational Christov Functions Collocation ‎Method
  K. Parand E. ‎Hajizadeh‎ A. Jahangiri S. Khaleqi
  The present study is an attempt to find a solution for Volterra's Population Model by utilizing Spectral methods based on Rational Christov functions. Volterra's model is a nonlinear integro-differential equation. First, the Volterra's Population Model is converted to a چکیده کامل

  The present study is an attempt to find a solution for Volterra's Population Model by utilizing Spectral methods based on Rational Christov functions. Volterra's model is a nonlinear integro-differential equation. First, the Volterra's Population Model is converted to a nonlinear ordinary differential equation (ODE), then researchers solve this equation (ODE). The accuracy of method is tested in terms of $RES$ error and compare the obtained results with some well-known results.The numerical results obtained show that the proposed method produces a convergent ‎solution.‎ پرونده مقاله
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  2 - Solving nonlinear Lane-Emden type equations with unsupervised combined artificial neural networks
  K. Parand Z. Roozbahani F. Bayat Babolghani
  In this paper we propose a method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-innite domain. The proposed approach is based on an Unsupervised Combined Articial Neural Networks (UCANN چکیده کامل

  In this paper we propose a method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-innite domain. The proposed approach is based on an Unsupervised Combined Articial Neural Networks (UCANN) method. Firstly, The trial solutions of the differential equations are written in the form of feed-forward neural networks containing adjustable parameters (the weights and biases); results are then optimized with the combined neural network. The proposed method is tested on series of Lane-Emden differential equations and the results are reported. Afterward, these results are compared with the solution of other methods demonstrating the eciency and applicability of the proposed method. پرونده مقاله