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By H b. 1855 Drinkwater

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In addition those algorithms corresponding to the choices (ii) and (iii) above have no difficulty in picking up appropriate boundary data. This is usually a major problem when employing an LOD method. The stability, convergence and possible usefulness of LOD hopscotch schemes is discussed in the manuscript by Gourlay and Morris (1973). 48 3. Hopscotch for the Wave Equation Recently Orley and McKee (1973) have considered the possibility of using hopscotch difference schemes for problems of the form $2u - - = L (6) u, ~t 2 ~4 [ In fact their analysis only considered the case of L z - - - .

IND is used to indicate which case is to be considered. With these constructs, and the exit facility, we do not need any labels or any GOTO statements. our case). However, we are forced to use existing languages (mostly Fortran in We have therefore decided to use these languages only in a very disci- plined way, so that the basic constructs are implemented only in a very restricted way. Our conventions in using Fortran are so restrictive that, if you know the simple and rather obvious rules that have been imposed, it is possible to understand our programs even if all the statement numbers and GOTO statements have been removed.

4. G. H. E. E. Sedgwick, "DETEST: A Program for Comparing Numerical Methods for Ordinary Differential Equations", Technical Report, Department of Computer Science, University of Toronto, in preparation. 63 5. E. Hull, "The Numerical Integration of Ordinary Differential Equations", IFIP Congress 68, Proceedings, (North-Holland, Amsterdam, 1968), pp. 131-144. 6. E. Hull, "The Effectiveness of Numerical Methods for Ordinary Differential Equations", SIAM Studies in Num Anal 2 (1970), pp. 114-121. 7.

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