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Somayeh Nemati

Somayeh Nemati

Academic rank: Associate Professor
ORCID:
Education: PhD.
ScopusId:
Faculty: Faculty of Mathematical Sciences
Address:
Phone: 01135302419

Research

Title
Matrix method based on the second kind Chebyshev polynomials for solving time fractional diffusion-wave equations
Type
JournalPaper
Keywords
Fractional diffusion-wave equations, Damping, Second kind Chebyshev polynomials, Operational matrix , Matrix equation
Year
2016
Journal Journal of Applied Mathematics and Computing
DOI
Researchers Somayeh Nemati ، Salameh Sedaghat

Abstract

In this paper, the second kind Chebyshev polynomials (SKCPs) basis is used to solve time-fractional diffusion-wave equations with damping. We present some notations and definitions of the fractional calculus and introduce some basic properties of the SKCPs. Bivariate shifted SKCPs are defined and the operational matrix of fractional integration and some other needed operational matrices are constructed. Our approach uses the properties of bivariate shifted SKCPs to transform the considered problem to a matrix equation without using any collocation points. The main characteristic of this technique is that only a small number of the basic functions is needed to obtain a satisfactory result. An estimation of the error is given in the sense of Sobolev norms. Numerical examples are given to demonstrate the efficiency and accuracy of the proposed method.