A piecewise spectral-collocation method for solving fractional Riccati differential equation in large domains

Abstract

This paper addresses the approximate solution of the fractional Riccati differential equation (FRDE) in large domains. First, the solution interval is divided into a finite number of subintervals. Then, the Legendre-Gauss-Radau points along with the Lagrange interpolation method are employed to approximate the FRDE solution in each subinterval. The method has the advantage of providing the approximate solutions in large intervals. Additionally, the convergence analysis of the numerical algorithm is also provided. Three illustrative examples are given to illustrate the efficiency and applicability of the proposed method.

Orthonormal piecewise Vieta-Lucas functions for the numerical solution of the one- and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations

“…In recent years, such basis functions have been widely used to solve various fractional problems. For instance, see [32] , [33] , [34] , [35] , [36] . In this study, we define the orthonormal piecewise Vieta-Lucas (VL) functions as a new family of the basis functions and employ them to solve the one- and two-dimensional piecewise fractional Galilei invariant advection–diffusion equations.…”

Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series

“…[32][33][34][35][36][37][38][39] as an example. The collocation method is one of the powerful spectral methods which are widely used for solving fractional differential and integro-differential equations [40][41][42][43][44]. Further, the numerical solution of delay and advanced DEs of arbitrary order has been reported by many researchers [45][46][47][48][49][50][51][52][53][54][55][56][57][58].…”