Visualitza Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC) per autoria "c64198f6-0936-4e17-b661-446e0b4cab8e"
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A general formula for the Magnus expansion in terms of iterated integrals of right-nested commutators
Arnal, A.; Casas, Fernando; Chiralt, Cristina IOP (2018-03)We present a general expression for any term of the Magnus series as an iterated integral of a linear combination of independent right-nested commutators with given coefficients. The relation with the Malvenuto–Reutenauer ... -
A note on the Baker–Campbell–Hausdorff series in terms of right-nested commutators
Arnal, A.; Casas, Fernando; Chiralt, Cristina Springer (2021-01-27)We get compact expressions for the Baker–Campbell–Hausdorff series Z = log(eX eY ) in terms of right-nested commutators. The reduction in the number of terms originates from two facts: (i) we use as a starting point an ... -
A Unifying Framework for Perturbative Exponential Factorizations
Arnal, A.; Casas, Fernando; Chiralt, Cristina; Oteo, José-Angel MDPI (2021-03-17)We propose a framework where Fer and Wilcox expansions for the solution of differential equations are derived from two particular choices for the initial transformation that seeds the product expansion. In this scheme, ... -
Applying splitting methods with complex coefficients to the numerical integration of unitary problems
Blanes, Sergio; Casas, Fernando; Escorihuela-Tomàs, Alejandro American Institute of Mathematical Sciences (AIMS) (2022)We explore the applicability of splitting methods involving complex coefficients to solve numerically the time-dependent Schr¨odinger equation. We prove that a particular class of integrators are conjugate to unitary ... -
Composition Methods for Dynamical Systems Separable into Three Parts
Casas, Fernando; Escorihuela-Tomàs, Alejandro MDPI (2020)New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into ... -
Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation
Bader, Philipp; Blanes, Sergio; Casas, Fernando MDPI (2019)A new way to compute the Taylor polynomial of a matrix exponential is presented which reduces the number of matrix multiplications in comparison with the de-facto standard Paterson-Stockmeyer method for polynomial ... -
Computing the matrix sine and cosine simultaneously with a reduced number of products
Seydaoğlu, Muaz; Bader, Philipp; Blanes, Sergio; Casas, Fernando Elsevier (2021-05)A new procedure is presented for computing the matrix cosine and sine simultaneously by means of Taylor polynomial approximations. These are factorized so as to reduce the number of matrix products involved. Two versions ... -
Continuous changes of variables and the Magnus expansion
Casas, Fernando; Chartier, Philippe; Murua, Ander IOP (2019-09-23)In this paper, we are concerned with a formulation of Magnus and Floquet-Magnus expansions for general nonlinear differential equations. To this aim, we introduce suitable continuous variable transformations generated by ... -
Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for nonautonomous linear evolution equations of parabolic type
Blanes, Sergio; Casas, Fernando; Thalhammer, Mechthild Oxford University Press (2018-04)The main objective of this work is to provide a stability and error analysis of high-order commutator-free quasi-Magnus (CFQM) exponential integrators. These time integration methods for nonautonomous linear evolution ... -
Efficient time integration methods for Gross-Pitaevskii equations with rotation term
Bader, Philipp; Blanes, Sergio; Casas, Fernando; Thalhammer, Mechthild American Institute of Mathematical Sciences (2019)The objective of this work is the introduction and investigation of favourable time integration methods for the Gross-Pitaevskii equation with rotation term. Employing a reformulation in rotating Lagrangian coordinates, ... -
Exponential Perturbative Expansions and Coordinate Transformations
Arnal, A.; Casas, Fernando; Chiralt, Cristina MDPI (2020)We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, the Floquet–Magnus expansion for periodic ... -
Families of efficient low order processed composition methods
Blanes, Sergio; Casas, Fernando; Escorihuela-Tomàs, Alejandro Elsevier (2024-10)New families of composition methods with processing of order 4 and 6 are presented and analyzed. They are specifically designed to be used for the numerical integration of differential equations whose vector field is ... -
Generalisation of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger type
Blanes, Sergio; Casas, Fernando; González, Cesáreo; Thalhammer, Mechthild Elsevier (2023-11-10)The present work is concerned with the extension of modified potential operator splitting methods to specific classes of nonlinear evolution equations. The considered partial differential equations of Schrödinger and ... -
High order integrators obtained by linear combinations of symmetric-conjugate compositions
Casas, Fernando; Escorihuela-Tomàs, Alejandro Elsevier (2022-02-01)A new family of methods involving complex coefficients for the numerical integration of differential equations is presented and analyzed. They are constructed as linear combinations of symmetric-conjugate compositions ... -
Novel symplectic integrators for the Klein-Gordon equation with space- and time-dependent mass
Bader, Philipp; Blanes, Sergio; Casas, Fernando; Kopylov, Nikita Elsevier (2019-04)We consider the numerical time-integration of the non-stationary Klein–Gordon equation with position- and time-dependent mass. A novel class of time-averaged symplectic splitting methods involving double commutators is ... -
Numerical integrators based on the Magnus expansion for nonlinear dynamical systems
Hajiketabi, M.; Casas, Fernando Elsevier (2020-03-15)Explicit numerical integration algorithms up to order four based on the Magnus expansion for nonlinear non-autonomous ordinary differential equations are presented and tested on problems possessing qualitative (very often, ... -
Preface for the special issue “Geometric numerical integration, twenty-five years later”
Blanes, Sergio; Casas, Fernando Taylor and Francis (2023) -
Runge–Kutta–Nyström symplectic splitting methods of order 8
Blanes, Sergio; Casas, Fernando; Escorihuela-Tomàs, Alejandro Elsevier (2022-12)Different families of Runge–Kutta–Nyström (RKN) symplectic splitting methods of order 8 are presented for second-order systems of ordinary differential equations and are tested on numerical examples. They show a better ... -
Splitting and composition methods in the numerical integration of differential equations
Blanes, Sergio; Murua, Ander; Casas, Fernando Sociedad Española de Matemática Aplicada (2008)We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field ... -
Splitting and composition methods with embedded error estimators
Blanes, Sergio; Casas, Fernando; Thalhammer, Mechthild Elsevier (2019-12)We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, ...