Extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind
Extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind
复制标题
求解第二类弱奇异非线性Volterra积分方程的外推法
DOI：
10.1016/j.jmaa.2005.12.013
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发表时间：
2006-12-01
影响因子：
1.3
通讯作者：
Huang Yong
中科院分区：
文献类型：
--
作者：
Lu Tao;Huang Yong
基于离散Gronwall不等式的一种新推广[L]。陶洪勇，离散Gronwall不等式的推广及其在第二类弱奇异Volterra积分方程中的应用，数学学报。分析的。应用数学，282(2003)56-62]，计算端点奇异积分的Navot正交规则[I]。关于欧拉-麦克劳林求和公式的进一步推广，数学学报。物理学报，41(1962)155-184]和[P.]A. Baratella， A. Palamara Orsi，弱奇异Volterra积分方程数值解的新方法，J.计算机学报。达成。数学，163(2004)401-418]，给出了求解第二类非线性弱奇异Volterra积分方程的一种新的正交方法。证明了近似解的收敛性和误差的渐近展开性，因此利用外推技术不仅得到了较高精度阶的近似，而且得到了误差的后验估计。(c) 2005爱思唯尔公司版权所有。
Based on a new generalization of discrete Gronwall inequality in [L. Tao, H. Yong, A generalization of discrete Gronwall inequality and its application to weakly singular Volterra integral equality of the second kind, J. Math. Anal. Appl. 282 (2003) 56-62], Navot's quadrature rule for computing integrals with the end point singularity in [I. Navot, A further extension of Euler-Maclaurin summation formula, J. Math. Phys. 41 (1962) 155-184] and a transformation in [P. Baratella, A. Palamara Orsi, A new approach to the numerical solution of weakly singular Volterra integral equations, J. Comput. Appl. Math. 163 (2004) 401-418], a new quadrature method for solving nonlinear weakly singular Volterra integral equations of the second kind is presented. The convergence of the approximation solution and the asymptotic expansion of the error are proved, so by means of the extrapolation technique we not only obtain a higher accuracy order of the approximation but also get a posteriori estimate of the error. (c) 2005 Elsevier Inc. All rights reserved.