6 papers · 1 filter
D-splitting methods: 2N -storage embedded explicit pseudo-geometric Runge-Kutta methods using splitting methods
Sergio Blanes, Alejandro Escorihuela-Tomà s
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…
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…
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…
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…
Generalized extrapolation methods based on compositions of a basic 2nd-order scheme
Sergio Blanes, Fernando Casas, Luke Shaw
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differe…
Families of efficient low order processed composition methods
Sergio Blanes, Fernando Casas, Alejandro Escorihuela-Tomà s
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…