P-stable high-order super-implicit and Obrechkoff methods for periodic initial value problems
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This paper discusses the numerical solution of periodic initial value problems. Two classes of methods are discussed, superimplicit and Obrechkoff. The advantage of Obrechkoff methods is that they are high-order one-step methods and thus will not require additional starting values. On the other hand they will require higher derivatives of the right-hand side. In cases when the right-hand side is very complex, we may prefer super-implicit methods. We develop a super-implicit P-stable method of order 12 and Obrechkoff method of order 18.
The article of record as published may be found at http://dx.doi.org/10.1016/j.camwa.2005.11.041
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