Shubha, V.S.George, S.Padikkal, P.2026-02-052019Journal of Applied Mathematics and Computing, 2019, 61, 46054, pp. 137-15315985865https://doi.org/10.1007/s12190-019-01246-1https://idr.nitk.ac.in/handle/123456789/24376We develop three third order derivative-free iterative methods to solve the nonlinear ill-posed oprerator equation F(x) = f approximately. The methods involve two steps and are free of derivatives. Convergence analysis shows that these methods converge cubically. The adaptive scheme introduced in Pereverzyev and Schock (SIAM J Numer Anal 43(5):2060–2076, 2005) has been employed to choose regularization parameter. These methods are applied to the inverse gravimetry problem to validate our developed results. © 2019, Korean Society for Computational and Applied Mathematics.Banach spacesInverse problemsNonlinear equationsAdaptive methodsCubic convegenceDerivative-free methodsLavrentiev regularizationsNonlinear ill-posed equationsIterative methods