Recursive collocation for the numerical solution of stiff ordinary differential equations
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 corresponding to a partition of I, by a linear combination of exponential functions. The function will involve only the "significant" eigenvalues (in a sense to be made precise) of the approximate Jacobian for . The unknown vectors in are computed recursively by requiring that satisfy the given system at certain suitable points in (collocation), with the additional condition that the collection of these functions represent a continuous function on I satisfying the given initial conditions.
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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