Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Numerical solution of ordinary differential equations using Legendre polynomial based Functional Link Artificial Neural Network (FLANN).It is a single layer neural network, so number of parameters is less than MLP and the hidden layer is eliminated by expanding the input pattern by Legendre polynomials.Unsupervised back propagation algorithm is used here.Obtained results are compared with the existing methods, plots and tables to show the porfulness of the methodology. , a new method based on single layer Legendre Neural Network (LeNN) model has been developed to solve initial and boundary value problems. In the proposed approach a Legendre polynomial based Functional Link Artificial Neural Network (FLANN) is developed. Nonlinear singular initial value problem (IVP), boundary value problem (BVP) and system of coupled ordinary differential equations are solved by the proposed approach to show the reliability of the method. The hidden layer is eliminated by expanding the input pattern using Legendre polynomials. Error back propagation algorithm is used for updating the network parameters (ights). Results obtained are compared with the existing methods and are found to be in good agreement.
['Susmita Mall', 'S. Chakraverty']
I am writing a research paper on a idea Application of Legendre Neural Network for solving ordinary differential equations
[{"from": "human", "value": "I am writing a research paper on a idea Application of Legendre Neural Network for solving ordinary differential equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Numerical solution of ordinary differential equations using Legendre polynomial based Functional Link Artificial Neural Network (FLANN).It is a single layer neural network, so number of parameters is less than MLP and the hidden layer is eliminated by expanding the input pattern by Legendre polynomials.Unsupervised back propagation algorithm is used here.Obtained results are compared with the existing methods, plots and tables to show the porfulness of the methodology. , a new method based on single layer Legendre Neural Network (LeNN) model has been developed to solve initial and boundary value problems. In the proposed approach a Legendre polynomial based Functional Link Artificial Neural Network (FLANN) is developed. Nonlinear singular initial value problem (IVP), boundary value problem (BVP) and system of coupled ordinary differential equations are solved by the proposed approach to show the reliability of the method. The hidden layer is eliminated by expanding the input pattern using Legendre polynomials. Error back propagation algorithm is used for updating the network parameters (ights). Results obtained are compared with the existing methods and are found to be in good agreement."}]