Application of the modified Newton's method to the solution of the fractional Riccati equation with the derivative of fractional variable order

• Тезисы на elibrary

 The article presents some aspects of the numerical analysis of the Cauchy problem for the fractional Riccati equation (FRE) with a derivative of a fractional variable order of the Gerasimov-Caputo type. The research tool is the modified Newton's method (MNM), which has local first-order convergence. In the work, a comparison of the results obtained by the MNM and by the explicit finite difference scheme (EFDS) was carried out. It is shown that MNM converges faster with a given accuracy than EFDS, although these methods have the same first order of convergence. Using Runge's rule, the computational accuracy of MNM and EFDS was estimated. It is shown that with an increase in the number of calculated grid nodes, the computational accuracy of the methods tends to unity. An example is given when the model fractional Riccati equation describes well the dynamics of the volumetric activity of radon in a saturated medium

Parovik R. I., Tverdyi D. A. Применение модифицированного метода Ньютона к решению дробного уравнения Риккати с производной дробного переменного порядка //Проблемы вычислительной и прикладной математики. – 2021. – №. 6. – С. 75-88.