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Mathematics of Computation

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Recursive collocation for the numerical solution of stiff ordinary differential equations


Author: H. Brunner
Journal: Math. Comp. 28 (1974), 475-481
MSC: Primary 65L05
DOI: https://doi.org/10.1090/S0025-5718-1974-0347089-9
MathSciNet review: 0347089
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Abstract: The exact solution of a given stiff system of nonlinear (homogeneous) ordinary differential equations on a given interval I is approximated, on each subinterval ${\sigma _k}$ corresponding to a partition ${\pi _N}$ of I, by a linear combination ${U_k}(x)$ of exponential functions. The function ${U_k}(x)$ will involve only the "significant" eigenvalues (in a sense to be made precise) of the approximate Jacobian for ${\sigma _k}$. The unknown vectors in ${U_k}(x)$ are computed recursively by requiring that ${U_k}(x)$ satisfy the given system at certain suitable points in ${\sigma _k}$ (collocation), with the additional condition that the collection of these functions $\{ {U_k}\}$ represent a continuous function on I satisfying the given initial conditions.


References [Enhancements On Off] (What's this?)

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Keywords: System of stiff nonlinear homogeneous ordinary differential equations, approximate solution by sums of exponential functions, recursive collocation, one-step methods
Article copyright: © Copyright 1974 American Mathematical Society