Computer simulation using particles
Computer simulation using particles
Moving point, particle, and free-Lagrange methods for convection-diffusion equations
SIAM Journal on Scientific and Statistical Computing
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Moving finite elements
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
A Krylov projection method for systems of ODEs
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
A semi-Lagrangian high-order method for Navier-Stokes equations
Journal of Computational Physics
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
Commutator-free Lie group methods
Future Generation Computer Systems - Special issue: Geometric numerical algorithms
A spectral element semi-Lagrangian (SESL) method for the spherical shallow water equations
Journal of Computational Physics
Runge-Kutta-Chebyshev projection method
Journal of Computational Physics
Symmetric Exponential Integrators with an Application to the Cubic Schrödinger Equation
Foundations of Computational Mathematics
Semi-Lagrangian multistep exponential integrators for index 2 differential-algebraic systems
Journal of Computational Physics
Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation
Journal of Computational Physics
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In this paper we consider the case of nonlinear convection-diffusion problems with a dominating convection term and we propose exponential integrators based on the composition of exact pure convection flows. These methods can be applied to the numerical integration of the considered PDEs in a semi-Lagrangian fashion. Semi-Lagrangian methods perform well on convection dominated problems (Pironneau in Numer. Math. 38:309---332, 1982; Hockney and Eastwood in Computer simulations using particles. McGraw-Hill, New York, 1981; Rees and Morton in SIAM J. Sci. Stat. Comput. 12(3):547---572, 1991; Baines in Moving finite elements. Monographs on numerical analysis. Clarendon Press, Oxford, 1994).In these methods linear convective terms can be integrated exactly by first computing the characteristics corresponding to the gridpoints of the adopted discretization, and then producing the numerical approximation via an interpolation procedure.