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Stability analysis of reducible quadrature methods for Volterra integro-differential equations
Applications of Mathematics, Tome 32 (1987) no. 1, pp. 37-48
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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 $y'(t)=\gamma y(t) + \int^t_0(\lambda + \mu t + vs) y(s) ds$ and absolute stability is deffined in terms of the real parameters $\gamma, \lambda, \mu$ and $v$. Sufficient conditions are illustrated for $(0;0)$ - methods and for combinations of Adams-Moulton and backward differentiation methods.
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 $y'(t)=\gamma y(t) + \int^t_0(\lambda + \mu t + vs) y(s) ds$ and absolute stability is deffined in terms of the real parameters $\gamma, \lambda, \mu$ and $v$. Sufficient conditions are illustrated for $(0;0)$ - methods and for combinations of Adams-Moulton and backward differentiation methods.
DOI : 10.21136/AM.1987.104234
Classification : 45J05, 45M10, 65Q05, 65R20
Keywords: backward-differentiation-formula method; Volterra integro-differential equations; theta method; test equation; stability; linear multistep methods; reducible quadrature formulas; linear difference equation; Adams-Moulton methods; stability of numerical solution 
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Bakke, Vernon L.; Jackiewicz, Zdzisław. Stability analysis of reducible quadrature methods for Volterra integro-differential equations. Applications of Mathematics, Tome 32 (1987) no. 1, pp. 37-48. doi: 10.21136/AM.1987.104234

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