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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
Operational matrices based on the shifted fifth-kind Chebyshev polynomials for solving nonlinear variable order integro-differential equations
Type
JournalPaper
Keywords
Shifted fifth-kind Chebyshev polynomials; Variable order; Nonlinear integro-differential equations; Operational matrix; Convergence analysis
Year
2021
Journal advances in difference equations
DOI
Researchers Hossein Jafari ، Somayeh Nemati ، Roghayeh Moallem Ganji

Abstract

In this research, we study a general class of variable order integro-differential equations (VO-IDEs). We propose a numerical scheme based on the shifted fifth-kind Chebyshev polynomials (SFKCPs). First, in this scheme, we expand the unknown function and its derivatives in terms of the SFKCPs. To carry out the proposed scheme, we calculate the operational matrices depending on the SFKCPs to find an approximate solution of the original problem. These matrices, together with the collocation points, are used to transform the original problem to form a system of linear or nonlinear algebraic equations. We discuss the convergence of the method and then give an estimation of the error. We end by solving numerical tests, which show the high accuracy of our results.