A Novel Method for Solving Ordinary Differential Equations with Artificial Neural Networks
نویسندگان
چکیده
This research work investigates the use of Artificial Neural Network (ANN) based on models for solving first and second order linear constant coefficient ordinary differential equations with initial conditions. In particular, we employ a feed-forward Multilayer Perceptron (MLPNN), but bypass standard back-propagation algorithm updating intrinsic weights. A trial solution equation is written as sum two parts. The part satisfies or boundary conditions contains no adjustable parameters. involves neural network to be trained satisfy equation. Numerous works have appeared in recent times regarding using ANN, however majority these employed single hidden layer perceptron model, incorporating weight updation. For homogeneous case, assume exponential form compute polynomial approximation statistical regression. From here pick unknown coefficients weights from input associated solution. To get output layer, algebraic default sign equations. We then apply Gaussian Radial Basis function (GRBF) model achieve our objective. obtained this manner need not adjusted. proceed develop MathCAD software, which enables us slightly adjust biases. compare convergence accuracy results analytic solutions, well well-known numerical methods obtain satisfactory example ODE problems.
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ژورنال
عنوان ژورنال: Applied mathematics
سال: 2021
ISSN: ['2152-7393', '2152-7385']
DOI: https://doi.org/10.4236/am.2021.1210059