SOLUTION OF EQUATION WITH FRIEDLY INTEGRALS BY COLLOCATION METHOD - Galimyanov, Anis; Gilemzyanov, Almaz; Minnegalieva, Chulpan (Revista Inclusiones, 2019)
This article describes a collocation method for solving an equation containing the fractional Riemann-Liouville integral of the form, form, где – regular integral, – known constant coefficients, – given as well – the desired function. An approximate solution is sought in the form of an algebraic polynomial. In constructing the computational scheme of the method, quadrature interpolation type formulas are used to calculate the fractional Riemann – Liouville integral, which were constructed in previous works of the authors. According to the collocation method, unknown coefficients are found by solving a system of linear equations of the collocation method. The substantiation of the constructed method is carried out, which implies the proof of the existence, the uniqueness of the approximate solution, and also its stability. A model equation was constructed and its numerical solution was performed by the indicated collocation method. The implementation of the method was carried out in the Wolfram Mathematica system.