Determination of a timewise potential in the wave equation with dynamic boundary condition from an additional measurement

Abstract

The objective of this paper is to determine the timewise potential coefficient numerically in the wave equation with initial and dynamic boundary conditions supplemented by additional measurement as an over-determination condition. The inverse identification problem considered in this work has a unique solution. However, it is ill-posed problem by being sensitive to noise. For the numerical realization, we apply the Crank-Nicolson FDM together with the Tikhonov regularization to find stable and accurate numerical solutions. The resulting nonlinear minimization problem is solved computationally using the MATLAB subroutine lsqnonlin. The present numerical results demonstrate that stable and accurate approximate solutions have been obtained.

Keywords

• Wave equation
• Inverse problem
• Dynamic boundary condition
• Additional measurement
• Tikhonov regularization
• Nonlinear optimization