Speeding up Newton-type iterations for stiff problems |
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Affiliation: | 1. Departamento de Análisis Matemático, Universidad de La Laguna, 38200 La Laguna-Tenerife, Spain;2. Area de Matemáticas, UNEG, Puerto Ordaz, Venezuela |
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Abstract: | Iterative schemes based on the Cooper and Butcher iteration [5] are considered, in order to implement highly implicit Runge–Kutta methods on stiff problems. By introducing two appropriate parameters in the scheme, a new iteration making use of the last two iterates, is proposed. Specific schemes of this type for the Gauss, Radau IA-IIA and Lobatto IIIA-B-C processes are developed. It is also shown that in many situations the new iteration presents a faster convergence than the original. |
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