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Implicit Two-Derivative Lobatto-Runge-Kutta collocation Methods for solution of stiff systems of first order initial value problems in ordinary differential equations are derived and studied.The inclusion of the second derivative terms in the methods enabled us to derive a set of methods which are stable,convergent with wide stability regions.Although the difficulty of calculating the second derivatives may be slightly higher than the first derivatives,the advantage gained makes them suitable for solving stable systems of stiff equations.Another requirement demands that the implicit two-derivatives high-order methods are to be implemented iteratively rather than directly in the usual way of the explicit Runge-Kutta methods,however,efficient methods for doing these are provided from the associated continuous schemes by their evaluations.The derived methods are illustrated by the applications to some test problems of stiff systems found in the liter ature and the numerical results obtained confirm the excellent potential of the implicit two-derivative methods.