โ Scribed by W.E. Baylis; S.J. Peel
No coin nor oath required. For personal study only.
Title of program: PCNUM Method of solution A predictor-corrector version of the Numerov method is Catalogue number: AARJ applied [1]. Step size is adjusted to maintain a specified accuracy, and solutions to homogeneous differential equa-Program obtainable from: CPC Program Library, Queen's tions can be stabilized by orthogonalization. University of Belfast, N. Ireland (see application form in this issue) Restrictions on the complexity of the problem The matrices y and F are assumed to be real matrices with Computer: IBM 370/3031;Installation: University of Windsor dimensions not exceeding 8 X 8 (they are not necessarily Computer Centre square). These restrictions may be removed at the cost of additional storage by adding appropriate COMPLEX*16 Operating system: OSMVT under VM type declarations on the one hand, and by increasing array dimensions on the other. Although F may be a nonlinear Programming language used: FORTRAN IV function of y, it is assumed that the /th column of F depends only on components in the corresponding column of y. As High speed storage required: 10 Kwords (for 8 channels) with other Numerov algorithms, the equations to be solved need to be written so that there are no first-order derivatives. No. of bits in a word: 32 Unusual features of the program Overlay structure: none The error monitored is the relative error in the local change of the independent variable, and this is compared with the No. of magnetic tapesrequired: none specified error limit to determine whether to halve, maintain or double the step size. Unlike other predictor-corrector Other peripherals used: card reader, line printer methods, no special starting procedure is required. Solutions to linear problems can be stabilized to ensure linear indepen-No. of cards in combined program and test deck: 829 dence The stabilization is accomplished by periodic orthogonalization of the columns of y with the frequency of appli-Card punchingcode: EBCDIC cation determined by the amount of change caused by the orthogonalization. Keywords: coupled second-order differential equations, nonlinear equations, predictor -corrector method, Numerov, Typical running rime scattering calculations Test runs with 4 channels (4 X 4 matrices) requiring evaluation at about 2500 points and stabilization, took 6 s to corn-Nature of the physical problem pile and 20 s to run on the IBM 370/3031. Matrix differential equations of the form References y (x) = Fix, y(x)], [1] W.E. Baylis and S.J. Peel, Comput. Phys. Commun. 25 are solved, including homogeneous equations such as arise in (1982) 7. quantum scattering theory.
๐ SIMILAR VOLUMES
A predictor-corrector scheme is developed for the numerical solution of the sine-Gordon equation using the method of lines approach. The solution of the approximating differential system satisfies a recurrence relation, which involves the cosine function. Pade' approximants are used to replace the c