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The paper presents the iterative solutions of two coefficient inverse problems (CIPs) arising in frequency sounding and electrical prospecting. An iterative algorithm is constructed to obtain such solutions. Exploiting the Beilina–Klibanov approach to CIPs, this algorithm possesses the new iterative and refinement procedures. These features enhance significantly both the spatial and contrast resolutions of reconstructed coefficients. The computational effectiveness of the proposed numerical technique is demonstrated in computational experiments with two applied CIPs: electromagnetic or acoustic frequency sounding and electrical prospecting of layered media. The Slichter–Langer–Tikhonov formulation is exploited as a mathematical model of the latter. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a simple, iteration free and easy-to-implement numerical algorithm for the solution of inverse Cauchy problem in linear or nonlinear elasticity. The bottom of a finite rectangular plate is imposed by overspecified boundary data, and we seek unknown data on the top side. A spring-damping transform method (SDTM) is introduced to the Navier equations, such that after a discretization by the differential quadrature method, we can apply a novel Lie-group integrator, namely the mixed group-preserving scheme (MGPS), to solve them as an initial value problem. Several numerical examples including nonlinear ones are examined to show that the MGPS can overcome the ill-posed behaviour of the inverse Cauchy problem in elasticity, which has good efficiency and stability against the noisy disturbance, even with an intensity large up toand. [ABSTRACT FROM AUTHOR]