Explicit parallel two-step peer methods
نویسندگان
چکیده
The construction of s-stage explicit parallel two-step peer methods for the solution of non-stiff initial value problems with optimal zero stability and order p = s is considered. By an additional condition superconvergence of order p = s + 1 can be achieved. Further criteria for good methods are large stability regions and small error constants. Corresponding parameter sets have been obtained using the differential evolution genetic algorithm. Numerical tests of the parallel peer methods in MATLAB and comparisons with ODE45 show the efficiency of the proposed methods already in a sequential implementation.
منابع مشابه
Parameter optimization for explicit parallel peer two-step methods
Due to a two-step structure certain explicit peer methods with s stages have a natural parallel implementation on s processors. By the peer property all stages have essentially identical properties and we construct a class of zerostable methods with order p = s in all stages. Two approaches are discussed for choosing the free parameters. In a certain subclass the stability polynomial depends on...
متن کاملAlgebraic criteria for A-stability of peer two-step methods
A new criterion for A-stability of peer two-step methods is presented which is verifiable exactly in exact arithmetic by checking semi-definiteness of a certain test matrix. It depends on the existence of two positive definite weight matrices for a given method. Although the initial approach is different using properties of the numerical radius the criterion itself resembles the one from algebr...
متن کاملExponentially Fitted Fifth-Order Two-Step Peer Explicit Methods
The so called peer methods for the numerical solution of Initial Value Problems (IVP) in ordinary differential systems were introduced by R. Weiner et al [6, 7, 11, 12, 13] for solving different types of problems either in sequential or parallel computers. In this work, we study exponentially fitted three-stage peer schemes that are able to fit functional spaces with dimension six. Finally, som...
متن کاملPersian Speakers’ Recognition of English Relative Clauses: The Effects of Enhanced Input vs. Explicit Feedback Types
Despite consensus in focus on form (FOF) instruction over the facilitative role of noticing, controversy has not quelled over ways of directing EFL learners’ attention towards formal features via implicit techniques like input-enhancement or explicit metacognitive feedback and interactive peer-editing on the output they produce. This quasi-experimental study investigated the impact of input enh...
متن کاملA new approach to control the global error of numerical methods for differential equations
Recently, Kulikov presented the idea of double quasi-consistency, which facilitates global error estimation and control, considerably. More precisely, a local error control implemented in doubly quasi-consistent numerical methods plays a part of global error control at the same time. However, Kulikov studied only Nordsieck formulas and proved that there exists no doubly quasi-consistent scheme ...
متن کامل