this paper presents an operational formulation of the tau method based upon orthogonal polynomials by using a reduced set of matrix operations for the numerical solution of nonlinear multi-order fractional differential equations(fdes). the main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of non-linear algebraic equations....

In this paper‎, ‎first‎, ‎a numerical method is presented for solving a class of linear Fredholm integro-differential equation‎. ‎The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions‎. ‎The application of the proposed operational matrix with tau method is then utilized to transform the integro-differential equations to...

In this work, the convection-diffusion integro-differential equation with a weakly singular kernel is discussed. The  Legendre spectral tau method is introduced for finding the unknown function. The proposed method is based on expanding the approximate solution as the elements of a shifted Legendre polynomials. We reduce the problem to a set of algebraic equations by using operational matrices....

in this paper, we adapt the operational tau method for personal computers and apply it to a system of two nonlinear second order ordinary differential equations which are related to general relativity. the interesting behaviour this problem exhibits in its numerical treatment is discussed. in this problem, we try to use the tau perturbation term to locate the correct solution of this nonlinear ...

In this paper, we adapt the operational Tau Method for personal computers and apply it to a system of two nonlinear second order ordinary differential equations which are related to general relativity. The interesting behaviour this problem exhibits in its numerical treatment is discussed. In this problem, we try to use the Tau perturbation term to locate the correct solution of this nonlin...

Abstract: In this work, the operational Tau method is presented to find the solutions of the linear and nonlinear Volterra-Fredholm-Hammerstein integral equations (VFHIEs) of the second kind. Some simple matrices in extension of Tau method for the numerical solutions of VFHIEs is applied. In fact, operational Tau method converts the integral parts of the desired VFHIEs to some operational matri...

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equ...