Parallel and sequential methods for ordinary differential equations
Parallel and sequential methods for ordinary differential equations
Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations
Applied Numerical Mathematics
Short note: a new minimum storage Runge-Kutta scheme for computational acoustics
Journal of Computational Physics
Optimizing locality and scalability of embedded Runge--Kutta solvers using block-based pipelining
Journal of Parallel and Distributed Computing
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This paper considers the parallel solution of large systems of ordinary differential equations (ODEs) which possess a special access pattern by explicit Runge---Kutta (RK) methods. Such systems may arise, for example, from the semi-discretization of partial differential equations (PDEs). We propose an implementation strategy based on a pipelined processing of the stages of the RK method that does not impose restrictions on the choice of coefficients of the RK method. This approach can be implemented with low storage while still allowing efficient step control by embedded solutions.