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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.

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