Geodesic
$A$-stable methods of high order for Volterra integral equations
Applications of Mathematics, Tome 20 (1975) no. 5, pp. 336-344
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Method for numerical solution of Volterra integral equations, based on the O.I.M. methods, is suggested. It is known that the class of O.I.M. methods includes $A$-stable methods of arbitrary high order of asymptotic accuracy. In part 5, it is proved that these methods generate methods for numerical solution of Volterra equations which are also $A$-stable and of an arbitrarily high order. There is one advantage of the methods. Namely, they need no matrix inversion in the course of their numerical realization.
Method for numerical solution of Volterra integral equations, based on the O.I.M. methods, is suggested. It is known that the class of O.I.M. methods includes $A$-stable methods of arbitrary high order of asymptotic accuracy. In part 5, it is proved that these methods generate methods for numerical solution of Volterra equations which are also $A$-stable and of an arbitrarily high order. There is one advantage of the methods. Namely, they need no matrix inversion in the course of their numerical realization.
DOI : 10.21136/AM.1975.103599
Classification : 45D05, 45L05, 65R05, 65R20
Keywords: $A$-stable methods 
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Malina, Ľubor. $A$-stable methods of high order for Volterra integral equations. Applications of Mathematics, Tome 20 (1975) no. 5, pp. 336-344. doi: 10.21136/AM.1975.103599

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