Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enforcing strong stability of explicit Runge--Kutta methods with
  superviscosity   A time discretization method is called strongly stable, if the norm of its
numerical solution is nonincreasing. It is known that, even for linear
semi-negative problems, many explicit Runge--Kutta (RK) methods fail to
preserve this property. In this paper, we enforce strong stability by modifying
the method with superviscosity, which is a numerical technique commonly used in
spectral methods. We propose two approaches, the modified method and the
filtering method for stabilization. The modified method is achieved by
modifying the semi-negative operator with a high order superviscosity term; the
filtering method is to post-process the solution by solving a diffusive or
dispersive problem with small superviscosity. For linear problems, most
explicit RK methods can be stabilized with either approach without accuracy
degeneration. Furthermore, we prove a sharp bound (up to an equal sign) on
diffusive superviscosity for ensuring strong stability. The bound we derived
for general dispersive-diffusive superviscosity is also verified to be sharp
numerically. For nonlinear problems, a filtering method is investigated for
stabilization. Numerical examples with linear non-normal ordinary differential
equation systems and for discontinuous Galerkin approximation of conservation
laws are performed to validate our analysis and to test the performance.

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The categories of this paper are: eess
27
The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
16
The categories of this paper are: stat
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The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th