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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
Analysis of the Euler and trapezoidal discretization methods for the numerical solution of nonlinear functional Volterra integral equations of Urysohn type
Type
JournalPaper
Keywords
Functional integral equationsVolterra–Urysohn integral equations, Picard iterative method, Gronwall inequality, Euler method, Trapezoidal method
Year
2021
Journal JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
DOI
Researchers ُُSohrab Bazm ، Pedro Lima ، Somayeh Nemati

Abstract

In this paper, we investigate nonlinear functional Volterra–Urysohn integral equations, a class of nonlinear integral equations of Volterra type. The existence and uniqueness of the solution to the equation is proved by a technique based on the Picard iterative method. For the numerical approximation of the solution, the Euler and trapezoidal discretization methods are utilized which result in a system of nonlinear algebraic equations. Using a Gronwall inequality and its discrete version, first order of convergence to the exact solution for the Euler method and quadratic convergence for the trapezoidal method are proved. To prove the convergence of the trapezoidal method, a new Gronwall inequality is developed. Finally, numerical examples show the functionality of the methods.