
Accession Number : AD0674479
Title : ON THE STABILITY AND CONVERGENCE OF THE SOCALLED 'FORWARD AND CENTERED FINITEDIFFERENCE' 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 TungHsien,
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 socalled 'forward and centered finitedifference' 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 finitedifference schemes are compared, and the analysis indicates that the widely used conventional system which employs forward finitedifference for the first time step and centered finitedifference for the rest of the computations gives the worst results, and is computationally unstable when lambda(= delta t/delta s) approaches 10.* This difficulty may be overcome by replacing the forward finitedifference 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