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On a class of modified Cayley--Magnus methods
Sergio Blanes, Fernando Casas, Arieh Iserles
We introduce a new class of numerical integrators for the time integration of non-autonomous linear ordinary differential equations whose coefficient matrix is sparse and evolves w…
D-splitting methods: 2N -storage embedded explicit pseudo-geometric Runge-Kutta methods using splitting methods
Sergio Blanes, Alejandro Escorihuela-Tomàs
Low-storage explicit Runge-Kutta schemes are particularly popular for the numerical integration of time-dependent partial differential equations based on the method-of-lines due to…
Splitting methods with complex coefficients for linear and nonlinear evolution equations
Sergio Blanes, Fernando Casas, Cesareo Gonzalez +1
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achie…
Families of efficient low order processed composition methods
Sergio Blanes, Fernando Casas, Alejandro Escorihuela-Tomàs
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 differen…
Symmetric-conjugate splitting methods for evolution equations of parabolic type
Sergio Blanes, Fernando Casas, Cesáreo González +1
The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional bene…
Splitting Methods for differential equations
Sergio Blanes, Fernando Casas, Ander Murua
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve t…