Splitting methods for three-dimensional bio-chemical transport
Applied Numerical Mathematics
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
Symplectic Methods Based on Decompositions
SIAM Journal on Numerical Analysis
Domain Decomposition Operator Splittings for the Solution of Parabolic Equations
SIAM Journal on Scientific Computing
Proceedings of the on Numerical methods for differential equations
Linearly implicit Runge—Kutta methods for advection—reaction—diffusion equations
Applied Numerical Mathematics
Applied Numerical Mathematics
Additive Runge-Kutta methods for the resolution of linear parabolic problems
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
Design and implementation of DIRK integrators for stiff systems
Applied Numerical Mathematics
Stability of ADI schemes applied to convection-diffusion equations with mixed derivative terms
Applied Numerical Mathematics
Applied Numerical Mathematics
Approximation for transient of nonlinear circuits using RHPM and BPES methods
Journal of Electrical and Computer Engineering
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Fractional step Runge-Kutta methods are a class of additive Runge-Kutta schemes that provide efficient time discretizations for evolutionary partial differential equations. This efficiency is due to appropriate decompositions of the elliptic operator involving the spatial derivatives. In this work, we tackle the design and analysis of embedded pairs of fractional step Runge-Kutta methods. Such methods suitably estimate the local error at each time step, thus providing efficient variable step-size time integrations. Finally, some numerical experiments illustrate the behaviour of the proposed algorithms.