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

Miglena N. Koleva () and Lubin G. Vulkov ()
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Miglena N. Koleva: Department of Mathematics, Faculty of Natural Sciences and Education, “Angel Kanchev” University of Ruse, 8 Studentska Str., 7017 Ruse, Bulgaria
Lubin G. Vulkov: Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, “Angel Kanchev” University of Ruse, 8 Studentska Str., 7017 Ruse, Bulgaria

Mathematics, 2025, vol. 13, issue 10, 1-18

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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