科研之友
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摘要
We present a regularization method for solving nonlinear ill-posed problems by applying the family of Runge-Kutta methods to an initial value problem, in particular, to the asymptotical regularization method. We prove that the developed iterative regularization method converges to a solution under certain conditions and with a general stopping rule. Some particular iterative regularization methods are numerically implemented. Numerical results of the examples show that the developed Runge-Kutta-type regularization methods yield stable solutions and that particular implicit methods are very efficient in saving iteration steps.
- 出版日期2008-4
