On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations

Journal Article · Wed May 01 00:00:00 EDT 1996 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/S1064827595282520· OSTI ID:231098

Abarbanel, S ^[1]; Gottlieb, D ^[2]; Carpenter, M H ^[3]

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1. Tel-Aviv Univ. (Israel)
2. Brown Univ., Providence, RI (United States). Division of Applied Mathematics
3. NASA Langley Research Center, Hampton, VA (United States)

The temporal integration of hyperbolic partial differential equations (PDEs) has been shown to lead sometimes to the deterioration of accuracy of the solution because of boundary conditions. A procedure for removal of this error in the linear case has been established previously. In this paper the authors consider hyperbolic PDEs (linear and nonlinear) whose boundary treatment is accomplished via the simultaneous approximation term (SAT) procedure. A methodology is presented for recovery of the full order of accuracy and has been applied to the case of a fourth-order explicit finite-difference scheme.

• Sponsoring Organization: USDOE
• OSTI ID: 231098
• Journal Information: SIAM Journal on Scientific Computing, Vol. 17, Issue 3; Other Information: PBD: May 1996
• Country of Publication: United States
• Language: English

Related Subjects

99 MATHEMATICS
COMPUTERS
INFORMATION SCIENCE
MANAGEMENT
LAW
MISCELLANEOUS
RUNGE-KUTTA METHOD
ACCURACY
PARTIAL DIFFERENTIAL EQUATIONS
NONLINEAR PROBLEMS
FINITE DIFFERENCE METHOD