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The extended Pouzet-Runge-Kutta methods for nonlinear neutral delay-integro-differential equations. (English) Zbl 1203.65289

The authors investigate stability properties for numerical methods of the class noted in the title, for the equations

d dtyt-Nyt-τ=ft,yt,yt-τ, t-τ t gt,ξ,yξdξ,tt 0 ,

with a function y(t) given on the interval [t 0 -τ,t 0 ], in a d-dimensional complex space. These compound methods are created on the base of the classical Runge-Kutta (RK) methods for nonlinear ordinary differential equations, and a Pouzet quadrature formula for integrals in the right-hand side of the equation to be solved. The “nonlinear stability” of the extended Pouzet-Runge-Kutta methods means global and asymptotical stability in the Lyapunov sense. The obtained nonlinear stability results are based on the concept of “algebraic stability” of RK-methods by K. Burrage and J. C. Butcher [BIT, Nord. Tidskr. Inf.-behandl. 20, 185–203 (1980; Zbl 0431.65051 )]. Numerical examples illustrate the theoretical results.

MSC:
65R20Integral equations (numerical methods)
45J05Integro-ordinary differential equations
45G10Nonsingular nonlinear integral equations
Software:
RODAS
References:
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