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Solution of Definite Integrals using Functional Link Artificial Neural Networks

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This paper discusses a new method to solve definite integrals using artificial neural networks. The objective is to build a neural network that would be a novel alternative to pre-established numerical methods and with the help of a learning algorithm, be able to solve definite integrals, by minimising a well constructed error function. The proposed algorithm, with respect to existing numerical methods, is effective and precise and well-suited for purposes which require integration of higher order polynomials. The observations have been recorded and illustrated in tabular and graphical form.

Satyasaran Changdar, Snehangshu Bhattacharjee• 2019

Related benchmarks

TaskDatasetResultRank
Numerical IntegrationDefinite integral of f(x) = x-1 over [0, 2]
Integral Value0.00e+0
2
Numerical IntegrationDefinite integral of f(x) = x^2 over [0, 2]
Integral Value2.66
2
Numerical IntegrationDefinite integral of f(x) = sqrt(1+x^2) over [0, 2]
Integral Value2.95
2
Numerical IntegrationDefinite integral of f(x) = sin x over [0, 2]
Integral Value1.29
2
Numerical IntegrationDefinite integral of f(x) = ln(x+1) over [0, 2]
Integral Value1.41
2
Numerical IntegrationDefinite integral of f(x) = 2^x over [0, 2]
Integral Value4.32
2
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