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Piecewise Linear Approximate Solution of Fractional Order Non-Stiff and Stiff Differential-Algebraic Equations by Orthogonal Hybrid Functions Based Numerical Method |
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PP: 183-200 |
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doi:10.18576/pfda/060303
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Author(s) |
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Seshu Kumar Damarla,
Madhusree Kundu,
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Abstract |
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| A simple yet effective numerical method using orthogonal hybrid functions consisting of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal triangular functions was proposed to numerically solve fractional order non- stiff and stiff differential-algebraic equations. The complementary generalized one-shot operational matrices, which are the foundation for the developed numerical method, were derived to estimate the Riemann-Liouville fractional order integral in the new orthogonal hybrid function domain. It was theoretically and numerically shown that the numerical method converges the approximate solutions to the exact solutions in the limit of step size tends to zero. Numerical examples were solved using the proposed method and the obtained results were compared with the results of some popular numerical techniques used for solving fractional order differential-algebraic equations in the literature. Our results were in good accordance with the results of the semi-analytical methods in case of non-stiff problems. In addition, our method provided valid approximate solution to stiff problem (fractional order version of Chemical Akzo Nobel problem) which the semi-analytical methods failed to solve. |
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