Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Godunov-mixed methods for advective flow problems in one space dimension
SIAM Journal on Numerical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
A generalized particle search-locate algorithm for arbitrary grids
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Exponential fitting BDF algorithms: explicit and implicit 0-stable methods
Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
Lagrange–Galerkin method for unsteady free surface water waves
Computing and Visualization in Science
A Spectral Stochastic Semi-Lagrangian Method for Convection-Diffusion Equations with Uncertainty
Journal of Scientific Computing
Applied Numerical Mathematics
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The accuracy and efficiency of several lower and higher order time integration schemes in Eulerian-Lagrangian computations are investigated for solution of convection-diffusion problems with nonlinear reaction terms. The implementation of these schemes differs from their Eulerian counterparts in the fact that they are applied during each time step, along the characteristic curves rather than in the time direction. The major focus is to examine the computational characteristics of a class of implicit, explicit, and implicit-explicit time marching methods combined with the Eulerian-Lagrangian procedure. The obtained results for several benchmark problems are considered to be representative, and might be helpful for a fair rating of solution schemes, particularly in long time computations.