Accession Number : AD0674479

Title :   ON THE STABILITY AND CONVERGENCE OF THE SO-CALLED 'FORWARD AND CENTERED FINITE-DIFFERENCE' SCHEMES FOR EQUATIONS OF THE FORM THE PARTIAL DERIVATIVE OF ZETA WITH RESPECT TO T + U THE PARTIAL DERIVATIVE OF ZETA WITH RESPECT TO X=O,

Corporate Author : EMMANUEL COLL BOSTON MASS ORIENTAL SCIENCE RESEARCH LIBRARY

Personal Author(s) : Liao Tung-Hsien,

Report Date : MAY 1968

Pagination or Media Count : 20

Abstract : With a view to solving equations of the form the partial derivative of zeta with respect to t + u the partial derivative of zeta with respect to x = 0 this paper first presents a discussion on the stability of the so-called 'forward and centered finite-difference' schemes under general circumstances and specifies the conditions for stability. The results are found to be different from those given by conventional techniques using centered differences. Three types of finite-difference schemes are compared, and the analysis indicates that the widely used conventional system which employs forward finite-difference for the first time step and centered finite-difference for the rest of the computations gives the worst results, and is computationally unstable when lambda(= delta t/delta s) approaches 1-0.* This difficulty may be overcome by replacing the forward finite-difference operations by the procedure of any one of the other two schemes. Furthermore, better results may be achieved by the introduction of an 'upwind analogue' in the second and the third scheme. (Author)

Descriptors :   (*WEATHER FORECASTING, *NUMERICAL ANALYSIS), (*PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS), WIND, ATMOSPHERIC MOTION, ATMOSPHERE MODELS, MATHEMATICAL MODELS, APPROXIMATION(MATHEMATICS), DIFFERENCE EQUATIONS, STABILITY, CONVERGENCE, CHINA

Subject Categories : Meteorology
      Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE