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In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of simpler linear differentialoperators and a nonlinear term. 相似文献
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B. Bujanda J. C. Jorge M. J. Moreta 《Numerical Methods for Partial Differential Equations》2012,28(2):597-620
We present a new class of efficient time integrators for solving linear evolution multidimensional problems of second‐order in time named Fractional Step Runge‐Kutta‐Nyström methods (FSRKN). We show that these methods, combined with suitable spliting of the space differential operator and adequate space discretizations provide important advantages from the computational point of view, mainly parallelization facilities and reduction of computational complexity. In this article, we study in detail the consistency of such methods and we introduce an extension of the concept of R‐stability for Runge‐Kutta‐Nyström methods. We also present some numerical experiments showing the unconditional convergence of a third order method of this class applied to resolve one Initial Boundary Value Problem of second order in time. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 597–620, 2012 相似文献
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In this work we design and analyze an efficient numerical method to solve two dimensional initial-boundary value reaction–diffusion
problems, for which the diffusion parameter can be very small with respect to the reaction term. The method is defined by
combining the Peaceman and Rachford alternating direction method to discretize in time, together with a HODIE finite difference
scheme constructed on a tailored mesh. We prove that the resulting scheme is ε-uniformly convergent of second order in time
and of third order in spatial variables. Some numerical examples illustrate the efficiency of the method and the orders of
uniform convergence proved theoretically. We also show that it is easy to avoid the well-known order reduction phenomenon,
which is usually produced in the time integration process when the boundary conditions are time dependent.
This research has been partially supported by the project MEC/FEDER MTM2004-01905 and the Diputación General de Aragón. 相似文献
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