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CONSTRUCTING NEW TIME INTEGRATORS USING INTERPOLATING POLYNOMIALS
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DOI：10.1137/18M1203808.png)
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We present a methodology for constructing time integrators for solving systems of first-order ordinary differential equations by using interpolating polynomials. Our approach is to combine ideas from complex analysis and approximation theory to construct new integrators. This strategy allows us to trivially satisfy order conditions and easily construct a range of implicit or explicit integrators with properties such as parallelism and high order of accuracy. In this work, we present several example polynomial methods including generalizations of the backward differentiation formula and Adams-Moulton methods. We compare the stability regions of these generalized methods to their classical counterparts and find that the new methods offer improved stability especially at high order.
Keyword:
time integration
polynomial interpolation
approximation theory
parallelism
high-order
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