Determination Force/Source Function Dependent on Space Under the Non-classical Condition Data

Abstract

In this present paper deal with an inverse force/source problem for a one-dimension wave equation under the non-classical condition with the right end displacement boundary as the additional measurement. Furthermore, inverse force/source problem comes from splitting wave equation, which is unstable while adding noise under the right end boundary condition. Numerical algorithm is based on finite different method (FDM) combine with separation variable. L-curve method and min norm is applied to reach regularization parameter where zeroth order Tikhonov regularization is proposed. Figures in section 3 are shown how accurate this unusual condition working in the wave equation.