Approximate Solutions for a Class of Nonlinear Fredholm and Volterra Integro-Differential Equations Using the Polynomial Least Squares Method

Bogdan Căruntu and Mădălina Sofia Paşca
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Bogdan Căruntu: Department of Mathematics, Politehnica University of Timişoara, 300006 Timişoara, Romania
Mădălina Sofia Paşca: Department of Mathematics, Politehnica University of Timişoara, 300006 Timişoara, Romania

Mathematics, 2021, vol. 9, issue 21, 1-13

Abstract: We apply the polynomial least squares method to obtain approximate analytical solutions for a very general class of nonlinear Fredholm and Volterra integro-differential equations. The method is a relatively simple and straightforward one, but its precision for this type of equations is very high, a fact that is illustrated by the numerical examples presented. The comparison with previous approximations computed for the included test problems emphasizes the method’s simplicity and accuracy.

Keywords: Volterra and Fredholm nonlinear integro-differential equations; approximate analytic polynomial solution; polynomial least squares method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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