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Ordinary differential equations: initial value problems

In: Numerical Analysis

Author

Listed:
  • Ian Jacques

    (Coventry Lanchester Polytechnic, Department of Mathematics)

  • Colin Judd

    (Coventry Lanchester Polytechnic, Department of Mathematics)

Abstract

Many mathematical models of physical problems result in the formulation of a first order ordinary differential equation of the form 7.1 $$ y' = f(x,y) $$ Here f is a given function of two real variables and y is an unknown function of the independent variable x. The general solution of (7.1) contains an arbitrary constant. In order to determine the solution uniquely, it is necessary to impose an additional condition on y. This usually takes the form 7.2 $$ y(x_0 ) = y_0 $$ for given numbers x0 and y0 and is known as an initial condition. Problems specified by (7.1) and (7.2) are called initial value problems. Sufficient conditions for the existence and uniqueness of such problems may be found in Rao (1981).

Suggested Citation

  • Ian Jacques & Colin Judd, 1987. "Ordinary differential equations: initial value problems," Springer Books, in: Numerical Analysis, chapter 7, pages 233-264, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-3157-2_7
    DOI: 10.1007/978-94-009-3157-2_7
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