非线性方程的求解—最优化样条函数康托诺维奇加权残值法

本文是得新提出的一种微分方程的新解法，最优化样条函数康托诺维奇加权残值法。来求解非线性微分方程。该法把优化理论引入微分方程的数值解法，揉最优化算法，加权残值法，样条函数法，康托诺维奇法于一体，具有精度高、收敛快、易于处理各种边界条件的优点，文中有基于原始微分方程的算例，对流体力学中Ｂｕｒｇｅｒｓ方程的成功求解，展示了该法的应用前景。

A NUMERICAL SOLUTION FOR THE NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS BY THE KANTOROVICH WEIGHTED RESIDUAL METHOD WITH OPTIMAL SPLINE FUNCTION

This paper suggests the use of the Kantorovich Weighted Residual Method with optimal splinefunction to solve nonlinear partial differential equations.By the introduction of the idea of the theory ofoptimum,combined with that of the Method of Spline Function,this Kantorovich Weighted ResidualMethod manifests the features that it has good percision,rapid convergency and convenient treatmentof boundary conditions.By this method,the nonlinear problem is readily solved and globe optimal pointcan be reliably found.In this paper,numerical examples are given which show that this method is ef-fective,especially in solving the Burgers equation in fluid mechanics.