<abstract xmlns="http://www.w3.org/1999/xhtml">In the paper, there has been constructed a discrete model of the non-classical Bittner operational calculus with a derivative understood as the operation <italic>S</italic><italic>b</italic>{x(k)} := {<italic>x(k</italic>+<italic>n)</italic> − <italic>b(k)x(k)</italic>}, which is a generalization of the <italic>n</italic>th-order forward difference. It has also been pointed out that there is a possibility to generalize operational calculus models with backward and central differences of higher orders.</abstract>

In the paper, there has been constructed a discrete model of the non-classical Bittner operational calculus with a derivative understood as the operation Sb{x(k)} := {x(k+n) − b(k)x(k)}, which is a generalization of the nth-order forward difference. It has also been pointed out that there is a possibility to generalize operational calculus models with backward and central differences of higher orders.

A Generalization of Difference Models of the Bittner Operational Calculus

Faculty of Mechanical and Electrical Engineering

Maritime Technical Journal

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"A Generalization of Difference Models of the Bittner Operational Calculus"}

In the paper, there has been constructed a discrete model of the non-classical Bittner operational calculus with a derivative understood as the operation...

A Generalization of Difference Models of the Bittner Operational Calculus

Published Online: Dec 31, 2019

Page range: 41 - 52

Received: Oct 18, 2019

Accepted: Dec 18, 2019

DOI: https://doi.org/10.2478/sjpna-2019-0024

Keywords
operational calculus, derivative, integrals, limit conditions, forward difference, backward difference, central difference

© 2019 Hubert Wysocki, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A Generalization of Difference Models of the Bittner Operational Calculus

Published Online: Dec 31, 2019

Page range: 41 - 52

Received: Oct 18, 2019

Accepted: Dec 18, 2019

DOI: https://doi.org/10.2478/sjpna-2019-0024

Keywordsoperational calculus, derivative, integrals, limit conditions, forward difference, backward difference, central difference

© 2019 Hubert Wysocki, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
operational calculus, derivative, integrals, limit conditions, forward difference, backward difference, central difference