首页|A new kernel-based approach for solving general fractional (integro)-differential-algebraic equations
A new kernel-based approach for solving general fractional (integro)-differential-algebraic equations
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Springer Nature
The recent introduction of the Least-Squares Support Vector Regression (LS-SVR) algorithm for solving differential and integral equations has sparked interest. In this study, we extend the application of this algorithm to address systems of differential-algebraic equations (DAEs) in general form. Our work presents a novel approach to solving general DAEs in an operator format by establishing connections between the LS-SVR machine learning model, weighted residual methods, and Legendre orthogonal polynomials. To assess the effectiveness of our proposed method, we conduct simulations involving various DAE scenarios, such as nonlinear systems, fractional-order derivatives, integro-differential, and partial DAEs. Finally, we carry out comparisons between our proposed method and currently established state-of-the-art approaches, demonstrating its reliability and effectiveness.
Least-squares support vector regressionDifferential-algebraic equationsFractional derivativeMachine learningWeighted residual methods
TayebehTaheri、Alireza Afzal Aghaei、Kourosh Pa rand
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Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C. Tehran, Iran
Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C. Tehran, Iran||Department of Cognitive Modeling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, G.C. Tehran, Iran||Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada
NETL
NSTL
Springer Nature
