A review of operational matrices and spectral techniques for fractional calculus
AH Bhrawy, TM Taha, JAT Machado - Nonlinear Dynamics, 2015 - Springer
Recently, operational matrices were adapted for solving several kinds of fractional
differential equations (FDEs). The use of numerical techniques in conjunction with …
differential equations (FDEs). The use of numerical techniques in conjunction with …
A method based on the Jacobi tau approximation for solving multi-term time–space fractional partial differential equations
In this paper, we propose and analyze an efficient operational formulation of spectral tau
method for multi-term time–space fractional differential equation with Dirichlet boundary …
method for multi-term time–space fractional differential equation with Dirichlet boundary …
[HTML][HTML] A new Jacobi operational matrix: an application for solving fractional differential equations
In this paper, we derived the shifted Jacobi operational matrix (JOM) of fractional derivatives
which is applied together with spectral tau method for numerical solution of general linear …
which is applied together with spectral tau method for numerical solution of general linear …
A fast and well-conditioned spectral method
S Olver, A Townsend - siam REVIEW, 2013 - SIAM
A spectral method is developed for the direct solution of linear ordinary differential equations
with variable coefficients and general boundary conditions. The method leads to matrices …
with variable coefficients and general boundary conditions. The method leads to matrices …
Connection formulae between generalized Lucas polynomials and some Jacobi polynomials: Application to certain types of fourth-order BVPs
WM Abd-Elhameed, YH Youssri - International Journal of Applied and …, 2020 - Springer
In this work, we give new explicit solutions for the connection problems between generalized
Lucas polynomial sequence and the two polynomials, namely third and fourth kinds of …
Lucas polynomial sequence and the two polynomials, namely third and fourth kinds of …
Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials
It is well known that for the discretization of the biharmonic operator with spectral methods
(Galerkin, tau, or collocation) we have a condition number of O (N8), where N is the number …
(Galerkin, tau, or collocation) we have a condition number of O (N8), where N is the number …
On solving systems of multi-pantograph equations via spectral tau method
SS Ezz-Eldien - Applied Mathematics and Computation, 2018 - Elsevier
The current manuscript focuses on solving systems of multi-pantograph equations. The
spectral tau method is applied for solving systems of multi-pantograph equations with shifted …
spectral tau method is applied for solving systems of multi-pantograph equations with shifted …
A fractional‐order Jacobi Tau method for a class of time‐fractional PDEs with variable coefficients
This paper presents a shifted fractional‐order Jacobi orthogonal function (SFJF) based on
the definition of the classical Jacobi polynomial. A new fractional integral operational matrix …
the definition of the classical Jacobi polynomial. A new fractional integral operational matrix …
[HTML][HTML] Shifted Jacobi spectral-Galerkin method for solving hyperbolic partial differential equations
Herein, we propose a numerical scheme to solve spectrally hyperbolic partial differential
equations (HPDEs) using Galerkin method and approximate the solutions using double …
equations (HPDEs) using Galerkin method and approximate the solutions using double …
[HTML][HTML] Jacobi spectral Galerkin method for distributed-order fractional Rayleigh–Stokes problem for a generalized second grade fluid
Distributed-order fractional differential operators provide a powerful tool for mathematical
modeling of multiscale multiphysics processes, where the differential orders are distributed …
modeling of multiscale multiphysics processes, where the differential orders are distributed …