Abstract

In this paper, a simple and convenient new regularization method which is called modified quasi-boundary value method for solving nonlinear backward heat equation is given. Some new quite sharp error estimates between the approximate solution are provided and generalize the results in our paper [Trong, Quan, Khanh, and Tuan, Zeitschrift Analysis und ihre Anwendungen 26: 231–245, 2007, Trong and Tuan, Electron. J. Diff. Eqns. 4: 1–10, 2006, Trong and Tuan, Electron. J. Diff. Eqns. 84: 1–12, 2008]. The approximation solution is calculated by the contraction principle. A numerical experiment is given.