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Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Neutral Delay Differential Equations

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  • Haiyan Yuan
  • Cheng Song
  • Peichen Wang

Abstract

This paper is devoted to the stability and convergence analysis of the two-step Runge-Kutta (TSRK) methods with the Lagrange interpolation of the numerical solution for nonlinear neutral delay differential equations. Nonlinear stability and D-convergence are introduced and proved. We discuss the -stability, -stability, and the weak -stability on the basis of -algebraically stable of the TSRK methods; we also discuss the D-convergence properties of TSRK methods with a restricted type of interpolation procedure.

Suggested Citation

  • Haiyan Yuan & Cheng Song & Peichen Wang, 2013. "Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Neutral Delay Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-14, May.
    • Handle: RePEc:hin:jnlmpe:683137
    DOI: 10.1155/2013/683137
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