An alternating group explicit iteration method of high accuracy is constructed for solving Burgers equation on the basis of physical sense of convection speed,and its stability and convergence are analysed by the linear method.Numeical results of the model problem are given.

Under the general initial-boundary-value condition and additional condition, the methods for solving problem of one-dimensional wave equation is discussed. The inverse problem is reduced to an ill-posed non-linear integral system. Tikhonov's regularization method overcomes the difficulty of inverse problem and has a good numerical stability. The Numerical results show that the method is feasible and effective.

In this paper, Discrete Newton Method for solving nonlinear operator equations and Tikhonov's regularization method for solving linear ill-posed problems are combined into a stable iterative scheme for solving nonlinear operator equations with hard computed and ill-conditioned derivatives. The results of convergence analyses and error estimates are ob-tained. The application of this method for solving the inverse problem on remote sensing of the thermal conductivity in the nonhomogeneous material is demonstrated. It is shown by numerical simulations that this method is feasible and effective.