时滞积分方程的高精度算法与外推加速收敛

High-Accuracy Algorithm and Extrapolation to Accelerate Convergence of Delay Integral Equation

通过对非整数节点采用插值技巧,得到了一个使用梯形公式的时滞积分方程数值新算法.新算法是一个高精度算法,其收敛阶可达O(h2).为达到更高精度,文中还采用外推技术,使收敛阶提高到O(h3).最后的数值算例很好的验证了理论结果.

In this paper, by using interpolation techniques for the non-integer node, we obtained a new numerical algorithm of delay integral equation by using trapezoid formula. The new algorithm is a high-accuracy algorithm, and its eon-vergencing order may be up to O（h^2）. In order to achieve greater precision order, this paper also uses extrapolation techniques, making the convergence order up to O（h^3）. The final numerical example verifies the theoretical results well.