Optimal error estimates for high order Runge-Kutta methods applied to evolutionary equations

Miscellaneous · Sun Jan 01 00:00:00 EST 1989

OSTI ID:5241289

McKinney, W R

Fully discrete approximations to 1-periodic solutions of the Generalized Korteweg de-Vries and the Cahn-Hilliard equations are analyzed. These approximations are generated by an Implicit Runge-Kutta method for the temporal discretization and a Galerkin Finite Element method for the spatial discretization. Furthermore, these approximations may be of arbitrarily high order. In particular, it is shown that the well-known order reduction phenomenon afflicting Implicit Runge Kutta methods does not occur. Numerical results supporting these optimal error estimates for the Korteweg-de Vries equation and indicating the existence of a slow motion manifold for the Cahn-Hilliard equation are also provided.

• Research Organization: Tennessee Univ., Knoxville, TN (United States)
• OSTI ID: 5241289
• Resource Relation: Other Information: Thesis (Ph. D.)
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
KORTEWEG-DE VRIES EQUATION
RUNGE-KUTTA METHOD
ERRORS
GALERKIN-PETROV METHOD
MATHEMATICAL MANIFOLDS
PROBABILISTIC ESTIMATION
DIFFERENTIAL EQUATIONS
EQUATIONS
ITERATIVE METHODS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
990200* - Mathematics & Computers