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Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Abstract Implicit-explicit (IMEX) linear multistep time-discretization schemes for partial differential equations have proved useful in many applications. However, they tend to have undesirableExpand
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Implicit-explicit methods for time-dependent partial differential equations
Implicit-explicit (IMEX) schemes have been widely used, especially in conjunction with spectral methods, for the time integration of spatially discretized partial differential equations (PDEs) ofExpand
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A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
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We present a new class of optimal high-order SSP and low-storage SSP Runge--Kutta schemes with s>p. Expand
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A simple embedding method for solving partial differential equations on surfaces
tl;dr
We develop a simple method for the numerical solution of partial differential equations (PDEs) on surfaces which embeds the problem within a Cartesian analog of the original equation, posed on the entire space containing the surface. Expand
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IMEX extensions of linear multistep methods with general monotonicity and boundedness properties
tl;dr
In this paper we consider implicit-explicit (IMEX) multistep methods for solving hyperbolic systems with stiff sources or relaxation terms. Expand
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Implicit-explicit methods for reaction-diffusion problems in pattern formation
Reaction-diffusion mechanisms have been used to explain pattern formation in developmental biology and in experimental chemical systems. To approximate the corresponding spatially discretized models,Expand
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Efficient Algorithms for Diffusion-Generated Motion by Mean Curvature
The problem of simulating the motion of evolving surfaces with junctions according to some curvature-dependent speed arises in a number of applications. By alternately diffusing and sharpeningExpand
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Implicit-Explicit Methods for Time-Dependent PDE''s
Implicit-explicit (IMEX) schemes have been widely used, especially in conjunction with spectral methods, for the time integration of spatially discretized PDEs of diffusion-convection type.Expand
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Global optimization of explicit strong-stability-preserving Runge-Kutta methods
tl;dr
We have studied explicit high-order strong-stability-preserving Runge-Kutta methods with downwind-biased spatial discretizations. Expand
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Diffusion-Generated Motion by Mean Curvature for Filaments
tl;dr
We generalize diffusion-generated motion by mean curvature to curvature motion of filaments, i.e., curves in R ^3, that may initially consist of a complex configuration of links. Expand
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