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非线性中立型延迟积分微分方程一般线性方法的稳定性分析

余越昕   

  1. 湘潭大学数学系, 湖南湘潭 411105
  • 收稿日期:2008-09-15 出版日期:2010-05-15 发布日期:2010-06-30
  • 基金资助:

    国家自然科学基金(10871164), 湖南省教育厅重点项目(09A093)及湖南省自然科学基金资助项目(08JJ6002)

余越昕. 非线性中立型延迟积分微分方程一般线性方法的稳定性分析[J]. 计算数学, 2010, 32(2): 125-134.

Yu Yuexin. STABILITY ANALYSIS OF GENERAL LINEAR METHODS FOR NONLINEAR NEUTRAL DELAY INTEGRO-DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2010, 32(2): 125-134.

STABILITY ANALYSIS OF GENERAL LINEAR METHODS FOR NONLINEAR NEUTRAL DELAY INTEGRO-DIFFERENTIAL EQUATIONS

Yu Yuexin   

  1. Department of Mathematics, Xiangtan University, Xiangtan 411105, Hunan, China
  • Received:2008-09-15 Online:2010-05-15 Published:2010-06-30
本文研究求解R(α,β1,β2,γ)类非线性中立型延迟积分微分方程的一般线性方法的数值稳定性,获得了代数稳定的一般线性方法稳定及渐近稳定的条件,最后的数值试验验证了所获理论的正确性.

 

This paper is concerned with the numerical stability of general linear methods for a class R(α,β1,β2,γ) of nonlinear neutral delay integro-differential equations. The sufficient conditions for the stability and asymptotic stability of algebraically stable general linear methods are derived. A numerical test is given to illustrate our result.

 

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