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

Thesis/Dissertation · Sat Dec 31 23:00:00 EST 1988

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
• Country of Publication: United States
• Language: English

Related Subjects

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