An implicit numerical spline method for systems for ODEs

Micula G.; Revnic A.

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An implicit numerical spline method for systems for ODEs

机译：ODE系统的隐式数值样条法

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An implicit numerical method is introduced that gives piecewise polynomial spline approximations for the solution of an initial value problem for the equation y'(t) = f(t, y(t)) Here, fis a function having continuous derivatives up to the order r. The method presented in this work, provides spline functions which approximate the solution of the problem in the most regular function space Cr+1. Error estimates in C and Cr+1 are given and the stability of the method is investigated. (C) 2000 Elsevier Science Inc. All rights reserved. [References: 7]

机译：引入了一种隐式数值方法，该方法为方程y'（t）= f（t，y（t））的初值问题的求解提供分段多项式样条曲线逼近，在此，fis函数具有直至阶的连续导数河在这项工作中提出的方法提供了样条函数，这些样条函数可以在最规则的函数空间Cr + 1中近似求解问题。给出了C和Cr + 1中的误差估计，并研究了该方法的稳定性。（C）2000 Elsevier Science Inc.保留所有权利。 [参考：7]

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《Applied mathematics and computation》 |2000年第1期|共12页
作者
Micula G.; Revnic A.;
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正文语种 eng
中图分类应用数学;
关键词
Deficient spline function; Implicit method; Stability condition; Stiff systems; Region of stability;

机译：样条函数不足;拟方法;稳定性条件;刚性系统;稳定性区域;

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专利

1. An implicit numerical spline method for systems for ODEs [J] . Micula G., Revnic A. Applied mathematics and computation . 2000,第1期

机译：ODE系统的隐式数值样条法
2. Numerical and Soft Computing Methods for Characteristic Value Problems of ODE and ODEs Systems [J] . Mehmet TarikAtay, BiagioSimonetti, Safa BozkurtCoskun, Mathematical Problems in Engineering: Theory, Methods and Applications . 2013,第5期

机译：ODE和ODEs系统特征值问题的数值和软计算方法
3. Numerical and Soft Computing Methods for Characteristic Value Problems of ODE and ODEs Systems [J] . Mehmet TarikAtay, BiagioSimonetti, Safa BozkurtCoskun, Mathematical Problems in Engineering: Theory, Methods and Applications . 2013,第2期

机译：ODE和ODEs系统特征值问题的数值和软计算方法
4. SOLVING THE BATEMAN EQUATIONS IN CASMO5 USING IMPLICIT ODE NUMERICAL METHODS FOR STIFF SYSTEMS [C] . Joshua M. Hykes, Rodolfo M. Ferrer International conference on mathematics and computational methods applied to nuclear science and engineering . 2013

机译：用刚度数值方法求解CASMO5中的贝特曼方程。
5. Finite element analysis using uniform B-spline approximation and implicit boundary method. [D] . Burla, Ravi Kumar. 2008

机译：使用均匀B样条逼近和隐式边界方法进行有限元分析。
6. Numerical Method Using Cubic B-Spline for a Strongly Coupled Reaction-Diffusion System [O] . Muhammad Abbas, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, -1

机译：三次B样条用于强耦合反应扩散系统的数值方法
7. Explicit and Implicit Methods for Numerical Solution of ODE [O] . Csoltkó Attila 100

机译：ODE数值解的显式和隐式方法
8. Stability of Numerical Methods for Solving Systems of Second Order ODE's [R] . Thomas, R. M. , Gladwell, I. 1981

机译：求解二阶ODE系统的数值方法的稳定性

An implicit numerical spline method for systems for ODEs

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