Splitting the one-Dimensional Wave Equation, Part II: Additional Data are Given by an End Displacement Measurement

  • Shilan Othman Hussein Department of Mathematics, College of Science, University of Sulaymaniyah, Sulaymaniyah, Iraq
  • M. S. Hussein Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Keywords: Measure one end boundary condition, Finite difference method, Separation of variables method, Regularization, Inverse force problem

Abstract

     In this research, an unknown space-dependent force function in the wave equation is studied. This is a natural continuation of [1] and chapter 2 of [2] and [3], where the finite difference method (FDM)/boundary element method (BEM), with the separation of variables method, were considered. Additional data are given by the one end displacement measurement. Moreover, it is a continuation of [3], with exchanging the boundary condition, where  are extra data, by the initial condition. This is an ill-posed inverse force problem for linear hyperbolic equation. Therefore, in order to stabilize the solution, a zeroth-order Tikhonov regularization method is provided. To assess the accuracy, the minimum error between exact and numerical solutions for the force is computed for various regularization parameters. Numerical results are presented and a good agreement was obtained for the exact and noisy data.

Published
2021-01-30
How to Cite
Hussein, S. O., & Hussein, M. S. (2021). Splitting the one-Dimensional Wave Equation, Part II: Additional Data are Given by an End Displacement Measurement. Iraqi Journal of Science, 62(1), 233-239. https://doi.org/10.24996/ijs.2021.62.1.22
Section
Mathematics