A system for the solution of initial and two-point boundary value problems

ABSTRACT

A programming system is described which accepts as input a formal description of a problem in ordinary differential equations and produces as output a program for solving that problem. It is capable of accepting arbitrary order, non-linear coupled sets of equations with initial conditions or the most general boundary conditions. Internal to the system is a package for performing symbolic algebra, and use is made of this in generating a program to do numerical work appropriate to the particular set of equations presented. This use of an algebra system thus makes sophisticated and powerful numerical techniques available to the non-specialist programmer.

REFERENCES

• 1: Barton, D., Willers, I.M., and Zahar, R.V.M., "Taylor Series methods for ordinary differential equations - an evaluation", Mathematical Software, edited by J. Rice, pp. 369 - 90, 1971, Academic Press, N.Y.
• 2: Barton, D., Willers, I.M., and Zahar, R.V.M., Computer Journal, 14, 243 - 8, 1971.
• 3: Fox, L., Numerical solution of two-point boundary value problems, 1957, Oxford University Press.
• 4: Hartree, D.R., Proc. Cam. Phil. Soc., 33, 223 - 39, 1937.
• 5: Picken, S.M., "algorithms for the solution of differential equations in Chebyshev series by the selected points method", Maths. 94, National Physical Laboratory, Division of Numerical and Applied Mathematics, 1970.
• 6: Willoughby, R., "Sparse Matrix algorithms and their relation to problem classes and computer architecture", RC2833, IBM Research Center, Yorktown Heights, 1970.
• 7: Richards, M. Proc. Spring Joint Computer Conference, 557 - 66, 1969.
• 8: A.N.S.I. Fortran, 1966, American National Standards Institute.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations

Additional Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.0 General

General Terms:
Theory

Keywords:
Algebraic manipulation, Differentiation, Ordinary differential equations, Symbolic algebra, Two point boundary value problems