Development of the Normal Spline Method for Linear Integro-Differential Equations

机译：线性积分微分方程法线样条法的发展

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The normal spline method is developed for the initial and boundary-value problems for linear integro-differential equations, probably being unresolved with respect to the derivatives, in Sobolev spaces of the arbitrary smoothness. It allows to solve a high-order systems without the reduction to first-order ones. The solving system can be arbitrary degenerate (with high differentiation index or irreducible to normal form). The method of nonuniform collocation grid creation for stiff problems is offered. Results of numerical solution to test problems are demonstrated.

机译：在任意光滑度的Sobolev空间中，针对线性积分-微分方程的初值和边值问题开发了法线样条法，该问题可能相对于导数尚未解决。它允许解决高阶系统而无需还原为一阶系统。求解系统可以是任意退化的（具有高微分指数或无法归结为正态形式）。提供了用于刚性问题的非均匀搭配网格创建方法。证明了测试问题的数值解的结果。

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《International Conference on Computational Science - ICCA 2003 Pt.2 Jun 2-4, 2003 Melbourne, Australia and St. Petersburg, Russia》|2003年|p.492-499|共8页
会议地点 Melbourne(AU) St. Petersburg(RU);Melbourne(AU) St. Petersburg(RU)
作者
Vladimir K. Gorbunov; Vyacheslav V. Petrischev; Vyacheslav Y. Sviridov;
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Ulyanovsk State University, L.Tolstoy street 42, 432970 Ulyanovsk, Russia;

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正文语种 eng
中图分类自动化技术、计算机技术;
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1. B-Spline collocation method for linear and nonlinear Fredholm and Volterra integro-differential equations [J] . Z. Mahmoodi, J. Rashidinia, E. Babolian Applicable Analysis . 2013,第9a10期

机译：线性和非线性Fredholm与Volterra积分微分方程的B样条搭配方法
2. Spline/Spectral Methods for Neutral Volterra Integro-Differential Equations with Delay [J] . H.M. El-Hawary, K.A. El-Shami Journal of applied sciences research . 2012,第11期

机译：时滞中立型Volterra积分微分方程的样条/谱方法
3. Tension spline collocation methods for singularly perturbed Volterra integro-differential and Volterra integral equations [J] . Vilmos Horvat, Mladen Rogina Journal of Computational and Applied Mathematics . 2002,第1a2期

机译：奇摄动的Volterra积分微分方程和Volterra积分方程的张力样条搭配方法
4. Development of the Normal Spline Method for Linear Integro-Differential Equations [C] . Vladimir K. Gorbunov, Vyacheslav V. Petrischev, Vyacheslav Y. Sviridov International Conference on Computational Science . 2003

机译：线性积分微分方程正常样条法的研制
5. Discontinuous Galerkin methods and cascading multigrid methods for integro-differential equations. [D] . Ma, Jingtang. 2004

机译：积分微分方程的间断Galerkin方法和级联多重网格方法。
6. A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things [O] . Rohul Amin, Shah Nazir, Iván García-Magariño 2020

机译：无线传感器网络与物联网非线性时滞积分微分方程数值解的配置方法
7. Development of the Normal Spline Method for Linear Integro-Differential Equations [O] . Vladimir K. Gorbunov, Vyacheslav V. Petrischev, Vyacheslav Y. Sviridov 2003

机译：线性积分微分方程正常样条法的研制
8. Linear Multistep Methods and the Construction of Quadrature Formulae for Volterra Integral and Integro-Differential Equations [R] . Wolkenfelt, P. H. M. 1979

机译：线性多步法与Volterra积分和积分微分方程的正交公式的构造

Development of the Normal Spline Method for Linear Integro-Differential Equations

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