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Second order semilinear Volterra integrodifferential equation in Banach space

Jan Bochenek (1992)

Annales Polonici Mathematici

By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of some semilinear second order Volterra integrodifferential equations in Banach spaces is proved. The results are applied to some integro-partial differential equations.

Stability analysis of reducible quadrature methods for Volterra integro-differential equations

Vernon L. Bakke, Zdzisław Jackiewicz (1987)

Aplikace matematiky

Stability analysis for numerical solutions of Voltera integro-differential equations based on linear multistep methods combined with reducible quadrature rules is presented. The results given are based on the test equation y ' ( t ) = γ y ( t ) + 0 t ( λ + μ t + v s ) y ( s ) d s and absolute stability is deffined in terms of the real parameters γ , λ , μ and v . Sufficient conditions are illustrated for ( 0 ; 0 ) - methods and for combinations of Adams-Moulton and backward differentiation methods.

Stability criteria of linear neutral systems with distributed delays

Guang-Da Hu (2011)

Kybernetika

In this paper, stability of linear neutral systems with distributed delay is investigated. A bounded half circular region which includes all unstable characteristic roots, is obtained. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded...

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