Abstract
A compiler program has been developed for the automatic computer solution of differential equations. The inputs to this compiler are FORTRAN statements of the equations (differential and algebraic) and of the initial and/or boundary conditions. The automatic computations are performed under a present error-limit, which is controlled by maintaining the integration stepsize to be well within the radius of convergence. The automatic solution is shown to be both faster and more accurate than standard techniques. This is achieved by using optimum stepsizes determined from the calculations of the radius of convergence at every step. This compiler program is particularly powerful in the solution of boundary-value problems and of “stiff” differential equations. This compiler program will accept up to 99 coupled 4-th order differential equations with ease.
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© 1974 Springer-Verlag
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Chang, Y.F. (1974). Automatic solution of differential equations. In: Colton, D.L., Gilbert, R.P. (eds) Constructive and Computational Methods for Differential and Integral Equations. Lecture Notes in Mathematics, vol 430. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066265
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DOI: https://doi.org/10.1007/BFb0066265
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