Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
Stable explicit schemes for equations of the Schro¨dinger type
SIAM Journal on Numerical Analysis
A numerical study of the nonlinear Schro¨dinger equation involving quintic terms
Journal of Computational Physics
SIAM Journal on Numerical Analysis
DuFort--Frankel-Type Methods for Linear and Nonlinear Schrödinger Equations
SIAM Journal on Numerical Analysis
Efficient finite difference solutions to the time-dependent Schrödinger equation
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Neural Networks - 2003 Special issue: Advances in neural networks research IJCNN'03
Solution of time-independent Schrödinger equation by the imaginary time propagation method
Journal of Computational Physics
Artificial neural networks for solving ordinary and partial differential equations
IEEE Transactions on Neural Networks
Training feedforward networks with the Marquardt algorithm
IEEE Transactions on Neural Networks
File access prediction using neural networks
IEEE Transactions on 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
Automatic parameter settings for the PROAFTN classifier using hybrid particle swarm optimization
AI'10 Proceedings of the 23rd Canadian conference on Advances in Artificial Intelligence
Solving differential equations with Fourier series and Evolution Strategies
Applied Soft Computing
Solving differential equations by means of feed-forward artificial neural networks
ICAISC'12 Proceedings of the 11th international conference on Artificial Intelligence and Soft Computing - Volume Part I
Computational Intelligence and Neuroscience
Comparison of artificial neural network architecture in solving ordinary differential equations
Advances in Artificial Neural Systems
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In this paper by using MultiLayer Perceptron and Radial Basis Function (RBF) neural networks, a novel method for solving both kinds of differential equation, ordinary and partial differential equation, is presented. From the differential equation and its boundary conditions, the energy function of the network is prepared which is used in the unsupervised training method to update the network parameters. This method was implemented to solve the nonlinear Schrodinger equation in hydrogen atom and triangle-shaped quantum well. Comparison of this method results with analytical solution and two well-known numerical methods, Runge-kutta and finite element, shows the efficiency of Neural Networks with high accuracy, fast convergence and low use of memory for solving the differential equations.