A variable timestep generalized Runge-Kutta method for the numerical integration of the space-time diffusion equations

Conference · Sun Sep 01 04:00:00 EDT 1991

OSTI ID:5930614

Aviles, B N; Sutton, T M; Kelly, III, D J

A generalized Runge-Kutta method has been employed in the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic timestep control. The efficiency of the Runge-Kutta method is enhanced by a block-factorization technique that exploits the sparse structure of the matrix system resulting from the space and energy discretized form of the time-dependent neutron diffusion equations. Preliminary numerical evaluation using a one-dimensional finite difference code shows the sparse matrix implementation of the generalized Runge-Kutta method to be highly accurate and efficient when compared to an optimized iterative theta method. 12 refs., 5 figs., 4 tabs.

• Research Organization: Knolls Atomic Power Lab., Schenectady, NY (United States)
• Sponsoring Organization: DOE; USDOE, Washington, DC (United States)
• DOE Contract Number: AC12-76SN00052
• OSTI ID: 5930614
• Report Number(s): KAPL-4731; CONF-920308--4; ON: DE92003010
• Country of Publication: United States
• Language: English

Related Subjects

663610* -- Neutron Physics-- (1992-)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE DIFFERENCE METHOD
ITERATIVE METHODS
MATHEMATICAL LOGIC
NEUTRON DIFFUSION EQUATION
NUMERICAL SOLUTION
RUNGE-KUTTA METHOD
SPACE-TIME
TIME DEPENDENCE