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Modified Multilag Methods for Volterra Functional Equations
P. H. M. Wolkenfelt
Mathematics of Computation
Vol. 40, No. 161 (Jan., 1983), pp. 301-316
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2007376
Page Count: 16
You can always find the topics here!Topics: Differential equations, Numerical quadratures, Approximation, Volterra equations, Ordinary differential equations, Mathematical integrals, Recurrence relations, Lipschitz condition, Polynomials, Error rates
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Linear multistep methods for ordinary differential equations in conjunction with a family of computationally efficient quadrature rules are employed to define a class of so-called multilag methods for the solution of Volterra integral and integro-differential equations. In addition, modified multilag methods are proposed which have the property that the stability behavior is independent of the choice of the quadrature rules. High order convergence of the methods is established. In particular, a special class of high order convergent methods is presented for the efficient solution of first-kind Volterra equations. Numerical experiments are reported.
Mathematics of Computation © 1983 American Mathematical Society