Motivated by studies on fully discrete numerical schemes for linear hyperbolic conservation laws, we present a framework on analyzing the strong stability of explicit Runge-Kutta (RK) time discretizations for seminegative autonomous linear systems. The analysis is based on the energy method and can be performed with the aid of a computer. Strong stability of various RK methods, including a sixteen-stage embedded pair of order nine and eight, has been examined under this framework. Based on numerous numerical observations, we further characterize the features of strongly stable schemes. A both necessary and sufficient condition is given for the strong stability of RK methods of odd linear order.
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Univ Massachusetts, Dept Math, 285 Old Westport Rd, N Dartmouth, MA 02747 USAUniv Massachusetts, Dept Math, 285 Old Westport Rd, N Dartmouth, MA 02747 USA
Bresten, Christopher
Gottlieb, Sigal
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Univ Massachusetts, Dept Math, 285 Old Westport Rd, N Dartmouth, MA 02747 USAUniv Massachusetts, Dept Math, 285 Old Westport Rd, N Dartmouth, MA 02747 USA
Gottlieb, Sigal
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Grant, Zachary
Higgs, Daniel
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机构:Univ Massachusetts, Dept Math, 285 Old Westport Rd, N Dartmouth, MA 02747 USA
Higgs, Daniel
Ketcheson, David I.
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机构:Univ Massachusetts, Dept Math, 285 Old Westport Rd, N Dartmouth, MA 02747 USA
Ketcheson, David I.
Nemeth, Adrian
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机构:Univ Massachusetts, Dept Math, 285 Old Westport Rd, N Dartmouth, MA 02747 USA
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Ohio State Univ, Dept Civil Environm & Geodet Engn, Columbus, OH 43210 USAOhio State Univ, Dept Civil Environm & Geodet Engn, Columbus, OH 43210 USA
Kubatko, Ethan J.
Yeager, Benjamin A.
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Ohio State Univ, Dept Civil Environm & Geodet Engn, Columbus, OH 43210 USAOhio State Univ, Dept Civil Environm & Geodet Engn, Columbus, OH 43210 USA
Yeager, Benjamin A.
Ketcheson, David I.
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4700 King Abdullah Univ Sci & Technol, Div Math & Comp Sci & Engn, Thuwal 23955, Saudi ArabiaOhio State Univ, Dept Civil Environm & Geodet Engn, Columbus, OH 43210 USA
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Oak Ridge Natl Lab, Computat Math Grp, Oak Ridge, TN 37830 USAUniv Massachusetts Dartmouth, Math Dept, 285 Old Westport Rd, N Dartmouth, MA 02747 USA
Grant, Zachary J.
Gottlieb, Sigal
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Univ Massachusetts Dartmouth, Math Dept, 285 Old Westport Rd, N Dartmouth, MA 02747 USAUniv Massachusetts Dartmouth, Math Dept, 285 Old Westport Rd, N Dartmouth, MA 02747 USA