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Mathematics of Computation

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One-step piecewise polynomial multiple collocation methods for initial value problems

Author: J. P. Hennart
Journal: Math. Comp. 31 (1977), 24-36
MSC: Primary 65L05
MathSciNet review: 0431686
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Abstract: New methods are proposed for the numerical solution of systems of first-order differential equations. On each subinterval of a given mesh of size h, a polynomial of degree l is constructed, its parameters being determined by a multiple collocation technique. The resulting piecewise polynomial approximation is of order $ O({h^{l + 1}})$ at the mesh points and between them. In addition, the jth derivatives of the approximation on each subinterval provide approximations of order $ O({h^{l + 1 - j}})$, $ j = 1, \ldots ,l$. Some of the methods proposed are shown to be A-stable or even strongly A-stable.

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Keywords: Initial value problems, ordinary differential equations, piecewise polynomials, collocation methods, A-stability
Article copyright: © Copyright 1977 American Mathematical Society

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