Galerkin/Runge-Kutta discretizations for parabolic partial differential equations
Efficient, high-order Galerkin/Runge-Kutta methods are constructed and analyzed for certain classes of parabolic initial boundary-value problems. In particular, the partial differential equations considered are (1) semilinear, (2) linear with time dependent coefficients, and (3) quasilinear. Optimal-order error estimates are established for each case. Also, for the problems in which the time-stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the optimal-order convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time-independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low-order method.
- Research Organization:
- Tennessee Univ., Knoxville (USA)
- OSTI ID:
- 5271422
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
BOUNDARY-VALUE PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
RUNGE-KUTTA METHOD
ALGORITHMS
ERRORS
ITERATIVE METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL LOGIC
NUMERICAL SOLUTION
990230* - Mathematics & Mathematical Models- (1987-1989)