TY - JOUR
T1 - Diagonally implicit multistage integration methods for pseudospectral solutions of the wave equation
AU - Jackiewicz, Zdzislaw
AU - Renaut, Rosemary
N1 - Funding Information:
This work was supported by the National (Z. Jackiewicz) and DMS-9402943 (R.A. Renaut).
Funding Information:
Foundation under grants
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2000/7
Y1 - 2000/7
N2 - Diagonally implicit multistage integration methods are employed for the numerical integration in time of first order hyperbolic systems arising from Chebyshev pseudospectral discretizations of the spatial derivatives in the wave equation. These methods have stage order q equal to the order p. The stage values can be utilized to recover approximations to the solution u of sufficiently high accuracy. The phenomenon of order reduction, which is present in the integration of differential systems by numerical methods of low stage order, such as explicit Runge-Kutta methods, is avoided.
AB - Diagonally implicit multistage integration methods are employed for the numerical integration in time of first order hyperbolic systems arising from Chebyshev pseudospectral discretizations of the spatial derivatives in the wave equation. These methods have stage order q equal to the order p. The stage values can be utilized to recover approximations to the solution u of sufficiently high accuracy. The phenomenon of order reduction, which is present in the integration of differential systems by numerical methods of low stage order, such as explicit Runge-Kutta methods, is avoided.
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U2 - 10.1016/S0168-9274(99)00129-4
DO - 10.1016/S0168-9274(99)00129-4
M3 - Conference article
AN - SCOPUS:0034229469
VL - 34
SP - 219
EP - 229
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
SN - 0168-9274
IS - 2
T2 - Auckland Numerical Ordinary Differential Equations (ANODE 98 Workshop)
Y2 - 29 June 1998 through 10 July 1998
ER -