High-order splitting methods for separable non-autonomous parabolic equations

We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coeffi- cients of order greater than two necessarily have negative coefficients). We propose to consider a class of methods that allows us to evaluate all time-dependent operators at real values of the time, leading to schemes which are stable and simple to implement. If the system can be considered as the perturbation of an exactly solvable problem and the flow of the dominant part is advanced using real coefficients, it is possible to build highly efficient methods for these problems. We show the performance of this class of methods on several numerical examples and present some new improved schemesThe authors thank the referees for their suggestions to improve the presentation of this work. The work of Sergio Blanes has been supported by Ministerio de Ciencia e Innovacion (Spain) under project MTM2010-18246-C03 and the Ministerio de Educacion, Cultura y Deporte, under Programa Nacional de Movilidad de Recursos Humanos del Plan Nacional de I-D+i 2008-2011 (PRX12/00547). The work of Muaz Seydaoglu has been supported by the Turkish Council of High Education through a grant for visiting the Instituto de Matematica Multidisciplinar at the Polytechnic University of Valencia where this work was carried out.Seydaoglu, M.; Blanes Zamora, S. (2014). High-order splitting methods for separable non-autonomous parabolic equations. Applied Numerical Mathematics. 84:22-32. doi:10.1016/j.apnum.2014.05.004S22328