On the numerical solution of boundary value problems for linear ordinary differential equations

ABSTRACT

A numerical method is presented for the solution of boundary value problems involving linear ordinary differential equations. The method described is noniterative and makes use of any one-step numerical integration scheme to reduce the problem from one of boundary values to one of initial values. Comments are made concerning some numerical results of applying the method to a specific problem. In addition an extension of the algorithm described to more general problems is discussed.

REFERENCES

• 1: BIRKHOFF, G., AND ROTA, G. Ordinary Differential Equations. Ginn and Co., 1962, 211.
• 2: CHANDRASEKHAR, S. Radiative Transfer. Dover Publications, Inc., New York, 1960.
• 3: COLLATZ, L. The Numerical Treatment of Differential Equations. Springer-Verlag, Berlin, 3d ed., 1960.
• 4: Fox, L. The Numerical Solution of Ordinary and Partial Differential Equations. Pergamon Press, London, 1962.
• 5: ----. The Numerical Solution of Two-point Boundary Problems in Ordinary Differential Equations. Oxford Univ. Press, 1957.
• 6: LANCE, G. Numerical Methods for High Speed Computers. Iliffe and Sons, Ltd., London, 1960.

INDEX TERMS

Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Linear systems (direct and iterative methods)
      G.1.7 Ordinary Differential Equations
          Subjects: Initial value problems; Boundary value problems

General Terms:
Algorithms, Design, Measurement, Performance, Theory