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. Therefore, the equation is converted to an algebraic system of the equations and by solving it, the solution of the equation is obtained. Further, the numerical example is given to illustrate the method’s efficiency.
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Shahsavari, M., Torkzadeh, L., & Nouri, K. (2023). Solving Abel’s equations with the shifted Legendre polynomials. Computational Methods for Differential Equations, 11(4), 865-875. doi: 10.22034/cmde.2023.52786.2222
MLA
Maryam Shahsavari; Leila Torkzadeh; Kazem Nouri. "Solving Abel’s equations with the shifted Legendre polynomials". Computational Methods for Differential Equations, 11, 4, 2023, 865-875. doi: 10.22034/cmde.2023.52786.2222
HARVARD
Shahsavari, M., Torkzadeh, L., Nouri, K. (2023). 'Solving Abel’s equations with the shifted Legendre polynomials', Computational Methods for Differential Equations, 11(4), pp. 865-875. doi: 10.22034/cmde.2023.52786.2222
VANCOUVER
Shahsavari, M., Torkzadeh, L., Nouri, K. Solving Abel’s equations with the shifted Legendre polynomials. Computational Methods for Differential Equations, 2023; 11(4): 865-875. doi: 10.22034/cmde.2023.52786.2222