Ordinary differential equations: initial value problems

Ian Jacques and Colin Judd
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Ian Jacques: Coventry Lanchester Polytechnic, Department of Mathematics
Colin Judd: Coventry Lanchester Polytechnic, Department of Mathematics

Chapter 7 in Numerical Analysis, 1987, pp 233-264 from Springer

Abstract: 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).

Date: 1987
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DOI: 10.1007/978-94-009-3157-2_7

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