GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
The development of Runge-Kutta methods for partial differential equations
Applied Numerical Mathematics - Special issue on selected keynote papers presented at 14th IMACS World Congress, Atlanta, NJ, July 1994
RKC: an explicit solver for parabolic PDEs
Journal of Computational and Applied Mathematics
Fourth Order Chebyshev Methods with Recurrence Relation
SIAM Journal on Scientific Computing
Projective Methods for Stiff Differential Equations: Problems with Gaps in Their Eigenvalue Spectrum
SIAM Journal on Scientific Computing
Telescopic projective methods for parabolic differential equations
Journal of Computational Physics
Explicit Time-Stepping for Stiff ODEs
SIAM Journal on Scientific Computing
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Construction of explicit runge-kutta pairs with stiffness detection
Mathematical and Computer Modelling: An International Journal
Projective and coarse projective integration for problems with continuous symmetries
Journal of Computational Physics
Journal of Scientific Computing
Heterogeneous Multiscale Methods for Mechanical Systems with Vibrations
SIAM Journal on Scientific Computing
Asymptotic-preserving Projective Integration Schemes for Kinetic Equations in the Diffusion Limit
SIAM Journal on Scientific Computing
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We introduce new projective versions of second-order accurate Runge-Kutta and Adams-Bashforth methods, and demonstrate their use as outer integrators in solving stiff differential systems. An important outcome is that the new outer integrators, when combined with an inner telescopic projective integrator, can result in fully explicit methods with adaptive outer step size selection and solution accuracy comparable to those obtained by implicit integrators. If the stiff differential equations are not directly available, our formulations and stability analysis are general enough to allow the combined outer-inner projective integrators to be applied to legacy codes or perform a coarse-grained time integration of microscopic systems to evolve macroscopic behavior, for example.