Boundary Value Techniques for the Numerical Solution of Certain Initial Value Problems in Ordinary Differential Equations

ABSTRACT

Linear initial value problems, particularly involving first order differential equations, can be transformed into systems of higher order and treated as boundary value problems. The type of difference equations used to replace the associated second order boundary value problem are yn - 2yn+1 + yn+2 = h2 ∑ &bgr;iy″n+i + h3; ∑ &dgr;iy‴n+i + · · ·, n = 1, 2, · · ·, N - 1 and - yN + yN+1 = h(b0y′N + b1y′N+1) + h2;(c0y″N + c1y″N+1) + · · ·. Numerical techniques referred to as M1, M2, and M3 have been developed in which error is O(h4), O(h6) and O(h8), respectively. Experimental results have been given to demonstrate the usefulness of method M3 over M1 or M2.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Boundary value problems

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Initial value problems

General Terms:
Experimentation, Measurement, Performance, Theory