论文标题
非线性逆问题的数值解的线性lavrent'ev积分方程
Linear Lavrent'ev Integral Equation for the Numerical Solution of a Nonlinear Coefficient Inverse Problem
论文作者
论文摘要
我们第一次为M.M.得出的Llinear积分方程开发了收敛的数值方法。 1964年，Lavrent'EV的目标是解决3D中波动方程的系数反问题。数据未确定。收敛分析与数值结果一起介绍。 Lavrent'ev方程的一个有趣的特征是，没有任何线性化，它将高度非线性系数的逆问题降低到第一个线性积分方程。然而，该方程式使用该系数逆问题生成的数据的数值结果显示出良好的重建精度。这与1951年得出的经典Gelfand-Levitan方程相似，该方程在1D情况下是有效的。
For the first time, we develop a convergent numerical method for the llinear integral equation derived by M.M. Lavrent'ev in 1964 with the goal to solve a coefficient inverse problem for a wave-like equation in 3D. The data are non overdetermined. Convergence analysis is presented along with the numerical results. An intriguing feature of the Lavrent'ev equation is that, without any linearization, it reduces a highly nonlinear coefficient inverse problem to a linear integral equation of the first kind. Nevertheless, numerical results for that equation, which use the data generated for that coefficient inverse problem, show a good reconstruction accuracy. This is similar with the classical Gelfand-Levitan equation derived in 1951, which is valid in the 1D case.
