Journal
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
Volume 95, Issue 3, Pages 528-539Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160.2017.1291932
Keywords
High-order fractional differential equation; power-series method; artificial neural network; criterion function; back-propagation learning algorithm
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Artificial neural networks afford great potential in learning and stability against small perturbations of input data. Using artificial intelligence techniques and modelling tools offers an ever-greater number of practical applications. In the present study, an iterative algorithm, which was based on the combination of a power series method and a neural network approach, was used to approximate a solution for high-order linear and ordinary differential equations. First, a suitable truncated series of the solution functions were substituted into the algorithm's equation. The problem considered here had a solution as a series expansion of an unknown function, and the proper implementation of an appropriate neural architecture led to an estimate of the unknown series coefficients. To prove the applicability of the concept, some illustrative examples were provided to demonstrate the precision and effectiveness of this method. Comparing the proposed methodology with other available traditional techniques showed that the present approach was highly accurate.
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