Neural algorithm for solving differential equations
Journal of Computational Physics
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Introduction to artificial neural systems
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Applied Mathematics and Computation
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
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Journal of Computational and Applied Mathematics
Neural Networks - 2003 Special issue: Advances in neural networks research — IJCNN'03
Modelling the dynamics of nonlinear partial differential equations using neural networks
Journal of Computational and Applied Mathematics
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Genetic Programming and Evolvable Machines
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Applied Soft Computing
IEEE Transactions on Neural Networks
Computers & Mathematics with Applications
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Mathematical and Computer Modelling: An International Journal
Solution of nonlinear ordinary differential equations by feedforward neural networks
Mathematical and Computer Modelling: An International Journal
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IEEE Transactions on Neural Networks
Neural-network methods for boundary value problems with irregular boundaries
IEEE Transactions on Neural Networks
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This paper investigates the solution of Ordinary Differential Equations (ODEs) with initial conditions using Regression Based Algorithm (RBA) and compares the results with arbitrary- and regression-based initial weights for different numbers of nodes in hidden layer. Here, we have used feed forward neural network and error back propagation method for minimizing the error function and for the modification of the parameters (weights and biases). Initial weights are taken as combination of randomas well as by the proposed regression based model. We present the method for solving a variety of problems and the results are compared. Here, the number of nodes in hidden layer has been fixed according to the degree of polynomial in the regression fitting. For this, the input and output data are fitted first with various degree polynomials using regression analysis and the coefficients involved are taken as initial weights to start with the neural training. Fixing of the hidden nodes depends upon the degree of the polynomial. For the example problems, the analytical results have been compared with neural results with arbitrary and regression based weights with four, five, and six nodes in hidden layer and are found to be in good agreement.