Selected papers from the international conference on Numerical solution of Volterra and delay equations
Boundary value methods based on Adams-type methods
NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
SIAM Journal on Numerical Analysis
Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Block-Boundary Value Methods for the Solution of Ordinary Differential Equations
SIAM Journal on Scientific Computing
Stability of Runge-Kutta methods for delay integro-differential equations
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
General Linear Methods for Volterra Integro-differential Equations with Memory
SIAM Journal on Scientific Computing
Stability of linear multistep methods for delay integro-differential equations
Computers & Mathematics with Applications
On the relations between B2V Ms and Runge-Kutta collocation methods
Journal of Computational and Applied Mathematics
Block boundary value methods for delay differential equations
Applied Numerical Mathematics
Block boundary value methods for solving Volterra integral and integro-differential equations
Journal of Computational and Applied Mathematics
Quadrature formulas descending from BS Hermite spline quasi-interpolation
Journal of Computational and Applied Mathematics
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In this paper, we construct a class of extended block boundary value methods (B"2VMs) for Volterra delay integro-differential equations and analyze the convergence and stability of the methods. It is proven under the classical Lipschitz condition that an extended B"2VM is convergent of order p if the underlying boundary value methods (BVM) has consistent order p. The analysis shows that a B"2VM extended by an A-stable BVM can preserve the delay-independent stability of the underlying linear systems. Moreover, under some suitable conditions, the extended B"2VMs can also keep the delay-dependent stability of the underlying linear systems. In the end, we test the computational effectiveness by applying the introduced methods to the Volterra delay dynamical model of two interacting species, where the theoretical precision of the methods is further verified.