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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
A new approach for solving integro-differential equations of variable order
Type
JournalPaper
Keywords
Integro-differential equations, Variable order, Shifted Legendre polynomials, Operational matrix, Collocation points
Year
2020
Journal JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
DOI
Researchers Roghayeh Moallem Ganji ، Hossein Jafari ، Somayeh Nemati

Abstract

In this work, we consider a class of nonlinear integro-differential equations of variable-order. Existence, uniqueness and stability results are discussed. For solving the considered equations, operational matrices based on the shifted Legendre polynomials are used. First, we approximate the unknown function and its derivatives in terms of the shifted Legendre polynomials. Then, by substituting these approximations into the equation and using the properties of the shifted Legendre polynomials together with the collocation points, the main problem is reduced to a system of nonlinear algebraic equations. An error bound is proved for the approximate solution obtained by the proposed method. Finally, some illustrative examples are included to show the efficiency and accuracy of the proposed scheme.