Numerical Determination of a Time-Dependent Source in a Modified Benjamin–Bona–Mahony Equation

Miglena N. Koleva; Lubin G. Vulkov

doi:10.3390/math13101618

and

¹

Department of Mathematics, Faculty of Natural Sciences and Education, “Angel Kanchev” University of Ruse, 8 Studentska Str., 7017 Ruse, Bulgaria

²

Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, “Angel Kanchev” University of Ruse, 8 Studentska Str., 7017 Ruse, Bulgaria

^*

Authors to whom correspondence should be addressed.

Mathematics2025, 13(10), 1618;https://doi.org/10.3390/math13101618

This article belongs to the Section E: Applied Mathematics

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Abstract

In this paper, we consider a modified Benjamin–Bona–Mahony (BBM) equation, which, for example, arises in shallow-water models. We discuss the well-posedness of the Dirichlet initial-boundary-value problem for the BBM equation. Our focus is on identifying a time-dependent source based on integral observation. First, we reformulate this inverse problem as an equivalent direct (forward) problem for a nonlinear loaded pseudoparabolic equation. Next, we develop and implement two efficient numerical methods for solving the resulting loaded equation problem. Finally, we analyze and discuss computational test examples.

Keywords:

Benjamin–Bona–Mahony equation; inverse source problem; integral observation; pseudoparabolic loaded equation; finite difference scheme

Numerical Determination of a Time-Dependent Source in a Modified Benjamin–Bona–Mahony Equation

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