第二类Volterra积分方程迭代配置解的渐近展开

ASYMPTOTIC EXPANSION OF ITERATED COLLOCATION SOLUTION FOR THE VOLTERRA INTEGRAL EQUATION OF SECOND KIND

讨论了第二类Ｖｏｌｔｅｒｒａ积分方程迭代配置法；证明了当使用分片ｐ—１次多项式进行配置时，迭代配置解可展开为步长ｈ的偶次幂，且首项为ｈ２Ｐ。利用这个渐近展式，可进行Ｒｉｃｈａｒｄｓｏｎ外推，提高逼近解的精度．

In this paper,numerical method of the iterated collocation for theVolterra integral equation of the second kind is considered.We show that whenpiecewise polynomials of degree p-1 are used, the iterated collocation solutionadmits an error expansion in even powers of the step -size h,beginning witha term in h2p By using this asymptotic expression,Richardson's extrapolationcan be done and the accuracy of numerical solution can also be improved.