APPROXIMATE SOLUTION FOR LINEAR INEGRO-DIFFERENTIAL EQUATION OF ORDER ONE BY LEGENDRE POLYNOMIALS - Yusupov, rabbim; SINDAROV, AKBAR (Журнал математики и информатики, 2021)
Aprroximate solution of linear integro differential equations (IDEs) of order one is presented based on the truncated series of Legendre polynomials. Reduction technique is applied to transform the IDEs into integral equations (IEs). Gauss Legendre quadrature formula is implemented to the kernel integrals and collocation method is used to fprm a system of linear algebraic equations . The collocation points are chosen as the roots of Legendre polynomials. The existence and uniqueness of the solution are shown. Rate of convergence of the proposed method is proved.