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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Miglena N. Koleva & Lubin G. Vulkov, 2025. "Numerical Determination of a Time-Dependent Source in a Modified Benjamin–Bona–Mahony Equation," Mathematics, MDPI, vol. 13(10), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1618-:d:1656150
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