Runge-Kutta methods for parabolic equations and convolution quadrature
We study the approximation properties of Runge-Kutta time discretizations of linear and semilinear parabolic equations, including incompressible Navier-Stokes equations. We derive asymptotically sharp error bounds and relate the temporal order of convergence, which is generally noninteger, to spatial regularity and the type of boundary conditions. The analysis relies on an interpretation of Runge-Kutta methods as convolution quadratures. In a different context, these can be used as efficient computational methods for the approximation of convolution integrals and integral equations. They use the Laplace transform of the confolution kernal via a discrete operational calculus. 23 refs., 2 tabs.
- OSTI ID:
- 6647500
- Journal Information:
- Mathematics of Computation; (United States), Journal Name: Mathematics of Computation; (United States) Vol. 60:201; ISSN 0025-5718; ISSN MCMPAF
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CALCULATION METHODS
CONVERGENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
EVALUATION
INTEGRAL EQUATIONS
INTEGRAL TRANSFORMATIONS
ITERATIVE METHODS
LAPLACE TRANSFORMATION
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARABOLAS
PARTIAL DIFFERENTIAL EQUATIONS
QUADRATURES
RUNGE-KUTTA METHOD
SHAPE
TRANSFORMATIONS