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BELLEN A.; JACKIEWICZ Z.; VERMIGLIO R.; ZENNARO M. 《IMA Journal of Numerical Analysis》1990,10(1):103-118
Stability analysis of Volterra-Runge-Kutta methods based onthe basic test equation of the form
where is a complex parameter, and on the convolution test equation
where and are real parameters, is presented. General stabilityconditions are derived and applied to construct numerical methodswith good stability properties. In particular, a family of second-orderVo-stable Volterra-Runge-Kutta methods is obtained. No Vo-stablemethods of order greater than one have been presented previouslyin the literature. 相似文献
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Stability analysis of multilag and modified multilag methodsfor Volterra integrodifferential equations is presented, withrespect to the nonconvolution test equation where , , µ, and are real parameters. The applicationof these methods to this test equation leads to difference equationswith variable coefficients which are of Poincar type. Usingthe extension of the Perron theorem, the conditions under whichthe solutions to such equations are bounded are derived. Asa consequence, a complete characterization of stability regionsof multilag and modified multilag methods with respect to theabove nonconvolution test equation is obtained. 相似文献
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Stability analysis of modified multilag methods for Volterraintegral equations of the second and first kind is presented,based respectively on the test equations
This analysis reinforces the opinion that modified multilagmethods are advantageous over quadrature methods for Volterraequations. They allow us to combine the good stability propertiesof backward differentiation formulae and the efficiency of Adams-Moultonformulae for ordinary differential equations. 相似文献
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