Abstract
In this paper a new technique for avoiding exact Jacobians in ROW methods is proposed. The Jacobiansf' n are substituted by matricesA n satisfying a directional consistency conditionA n f n =f' n f n +O(h). In contrast to generalW-methods this enables us to reduce the number of order conditions and we construct a 2-stage method of order 3 and families of imbedded 4-stage methods of order 4(3). The directional approximation of the Jacobians has been realized via rank-1 updating as known from quasi-Newton methods.
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Burmeister, W., Grossmann, C. & Scholz, S. Directional approximation of the jacobians in ROW-methods. BIT 31, 89–101 (1991). https://doi.org/10.1007/BF01952786
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DOI: https://doi.org/10.1007/BF01952786