A New Class of Time Discretization Schemes for the Solution of Nonlinear PDEs

1998/12/01 by Gregory Beylkin, James M. Keiser, Lev Vozovoi +1 · 14 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Numerical methods for differential equations #Differential Equations and Numerical Methods

paper · doi:10.1006/jcph.1998.6093

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• Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential\n integrators
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• Efficient semi-implicit numerical schemes preserving the original energy dissipation law for nonlocal phase field models
• Easy-to-Implement One-Step Schemes for Stochastic Integration
• Maximum principle preserving exponential time differencing schemes for the nonlocal Allen-Cahn equation
• Fourth-Order Time-Stepping for Stiff PDEs
• Maximum bound principles for a class of semilinear parabolic equations and exponential time differencing schemes
• Unconditionally stable exponential time differencing schemes for the mass-conserving Allen-Cahn equation with nonlocal and local effects
• Energy stable arbitrary order ETD-MS method for gradient flows with Lipschitz nonlinearity
• Effect of spatial configuration of an extended nonlinear Kierstead-Slobodkin reaction-transport model with adaptive numerical scheme. [europepmc]
• Sensor Selection and State Estimation for Unobservable and Non-Linear System Models. [europepmc]