Solving partial differential equations by collocation using radial basis functions
Applied Mathematics and Computation
Meshless Galerkin methods using radial basis functions
Mathematics of Computation
Solving a system of nonlinear integral equations by an RBF network
Computers & Mathematics with Applications
Unsupervised adaptive neural-fuzzy inference system for solving differential equations
Applied Soft Computing
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
A MLP solver for first and second order partial differential equations
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Application of feedforward neural network in the study of dissociated gas flow along the porous wall
Expert Systems with Applications: An International Journal
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Comparison of artificial neural network architecture in solving ordinary differential equations
Advances in Artificial Neural Systems
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In this paper a neural network for solving partial differential equations is described. The activation functions of the hidden nodes are the radial basis functions (RBF) whose parameters are learnt by a two-stage gradient descent strategy. A new growing RBF-node insertion strategy with different RBF is used in order to improve the net performances. The learning strategy is able to save computational time and memory space because of the selective growing of nodes whose activation functions consist of different RBFs. An analysis of the learning capabilities and a comparison of the net performances with other approaches have been performed. It is shown that the resulting network improves the approximation results.