TY - JOUR
ID - 15975
TI - Solving Abel’s equations with the shifted Legendre polynomials
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Shahsavari, Maryam
AU - Torkzadeh, Leila
AU - Nouri, Kazem
AD - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran.
Y1 - 2023
PY - 2023
VL - 11
IS - 4
SP - 865
EP - 875
KW - Abel’s equation
KW - Integral equation
KW - Caputo differential operator
KW - Shifted Legendre polynomial
DO - 10.22034/cmde.2023.52786.2222
N2 - 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.
UR - https://cmde.tabrizu.ac.ir/article_15975.html
L1 - https://cmde.tabrizu.ac.ir/article_15975_cd59407bcfd2b0c8e2fa282de1e91a2a.pdf
ER -