Reconstruction of a potential coefficient in the Rayleigh–Love equation with non-classical boundary condition

Abstract

PurposeThe purpose of this paper is to reconstruct the potential numerically in the fourth-order Rayleigh–Love equation with boundary and nonclassical boundary conditions, from additional measurement.Design/methodology/approachAlthough, the aforesaid inverse identification problem is ill-posed but has a unique solution. The authors use the cubic B-spline (CBS) collocation and Tikhonov regularization techniques to discretize the direct problem and to obtain stable as well as accurate solutions, respectively. The stability, for the discretized system of the direct problem, is also carried out by means of the von Neumann method.FindingsThe acquired results demonstrate that accurate as well as stable solutions for the a(t) are accessed for λ∈ {10–8, 10–7, 10–6, 10–5}, when p ∈ {0.01%, 0.1%} for both linear and nonlinear potential coefficient a(t). The stability analysis shows that the discretized system of the direct problem is unconditionally stable.Research limitations/implicationsSince the noisy data are introduced, the investigation and analysis model real circumstances where the practical quantities are naturally infested with noise.Practical implicationsThe acquired results demonstrate that accurate as well as stable solutions for the a(t) are accessed for λ∈ {10–8, 10–7, 10–6, 10–5}, when p ∈ {0.01%, 0.1%} for both linear and nonlinear potential coefficient a(t). The stability analysis shows that the discretized system of the direct problem is unconditionally stable.Originality/valueThe potential term in the fourth-order Rayleigh–Love equation from additional measurement is reconstructed numerically, for the first time. The technique establishes that accurate, as well as stable solutions are obtained.