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非线性中立型延迟积分微分方程线性Θ-方法的渐近稳定性

余越昕, 文立平   

  1. 湘潭大学数学系, 湖南湘潭 411105
  • 收稿日期:2006-12-06 出版日期:2009-12-15 发布日期:2009-12-30
  • 基金资助:

    国家自然科学基金资助项目(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, 文立平. 非线性中立型延迟积分微分方程线性Θ-方法的渐近稳定性[J]. 数值计算与计算机应用, 2009, 30(4): 241-246.

Yu Yuexin, Wen Liping. ASYMPTOTIC STABILITY OF LINEAR Θ-METHODS FOR NONLINEAR NEUTRAL DELAY INTEGRO-DIFFERENTIAL EQUATIONS[J]. Journal of Numerical Methods and Computer Applications, 2009, 30(4): 241-246.

ASYMPTOTIC STABILITY OF LINEAR Θ-METHODS FOR NONLINEAR NEUTRAL DELAY INTEGRO-DIFFERENTIAL EQUATIONS

Yu Yuexin, Wen Liping   

  1. Department of Mathematics, Xiangtan University, Xiangtan 411105, China
  • Received:2006-12-06 Online:2009-12-15 Published:2009-12-30
将线性θ-方法用于求解R(α,β1,β2,γ)类非线性中立型延迟积分微分方程,结果表明A-稳定的线性θ-方法(也即1/2≤ θ ≤ 1)是渐近稳定的,最后的数值试验验证了所获理论结果的正确性.

 

Linear θ-methods are adapted for solving a class R(α,β1,β2,γ) of nonlinear neutral delay integro-differential equations. It is proved that an A-stable linear θ-method (i.e. 1/2≤ θ ≤ 1) is asymptotic stability. Numerical test is given to confirm the theoretical results.

 

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