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,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1968
- Accession Number
- AD0674479
Entities
People
- Liao Tung-hsien
Organizations
- Emmanuel College