An Algorithm for the Closed-Form Solution of Certain Classes of Volterra–Fredholm Integral Equations of Convolution Type

Autor:	Efthimios Providas
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	integral equations Volterra–Fredholm equations nonlinear equations closed-form solution convolution kernels Laplace transform Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
Zdroj:	Algorithms, Vol 15, Iss 6, p 203 (2022)
Druh dokumentu:	article
ISSN:	1999-4893
DOI:	10.3390/a15060203
Popis:	In this paper, a direct operator method is presented for the exact closed-form solution of certain classes of linear and nonlinear integral Volterra–Fredholm equations of the second kind. The method is based on the existence of the inverse of the relevant linear Volterra operator. In the case of convolution kernels, the inverse is constructed using the Laplace transform method. For linear integral equations, results for the existence and uniqueness are given. The solution of nonlinear integral equations depends on the existence and type of solutions ofthe corresponding nonlinear algebraic system. A complete algorithm for symbolic computations in a computer algebra system is also provided. The method finds many applications in science and engineering.
Databáze:	Directory of Open Access Journals
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