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A Variant of Accelerated Ramadan Group Adomian Decomposition Method for Numerical Solution of Fractional Riccati Differential Equations |
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PP: 663-675 |
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doi:10.18576/pfda/100410
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Author(s) |
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Ahmed Abdelaziz Elsayed,
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Abstract |
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| Due to the vast range of applications in many scientific c domains, researchers have recently become
interested in quadratic Riccati differential equations of fractional order and their solutions. In
this research, we propose a new method for solving particular classes of quadratic Riccati fractional
differential equations that combine the Ramadan group transform (RGT) and a variant of the
accelerated Adomian decomposition method (AADM). It is worth noting that RGT is a generalization
for both Laplace and Sumudu transforms. El-kalla proposed the AADM, where the main
advantages of AADM are that the polynomials generated are recursive and do not have derivative
terms, so the formula is easy to programme and saves much time on the same processor as the
traditional Adomian polynomials formula, and thus the solution obtained using this proposed hybrid
method accelerated Ramadan group Adomian decomposition method (RGAADM), converges
faster than the traditional Adomian decomposition method According to the findings of this work,
the solutions obtained by solving a class of quadratic Riccati differential equations of fractional order
are extremely compatible with those found via exact solutions. We obtained good performance
in all applied cases, which may lead to a promising strategy for many applications. |
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