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Solving Abel's equations with the shifted Legendre polynomials
2023Summary: In this article, a numerical method is presented to solve Abel's equations. In the given method, the solution of the equation is found as a finite expansion of the shifted Legendre polynomials. To this end, the integral and differential parts of the equation are converted to vector-matrix representations.
Shahsavari, maryam +2 more
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Rational solutions of Abel trigonometric polynomial differential equations
Journal of Geometry and Physics, 2022This paper deals with the trigonometric polynomial differential equations of the form \[ Y' = A(\theta) Y^2 + B(\theta) Y^3, \] where \(A\) and \(B\) are real trigonometric polynomials with \(B(\theta) \not\equiv 0\). This paper proves that these equations have at most two trigonometric polynomial solutions, and further shows that such solutions are ...
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Numerical Approach of Fractional Abel Differential Equation by Genocchi Polynomials
International Journal of Applied and Computational Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fariba Rigi, Haleh Tajadodi
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Exact and Numerical Solution of Abel Integral Equations by Orthonormal Bernoulli Polynomials
International Journal of Applied and Computational Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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