Abstract

Asymptotic solutions of a class of nonlinear boundary‐value problems are studied. The problem is a model arising in nuclear energy distribution. For large values of the parameter, the differential equations are of the singular‐perturbation type and approximations are constructed by the method of matched asymptotic expansions.

Highlights

  • Many of the problems occurlng in physics, engineering and applied mathematics contain a small parameter, and due to difficulties such as nonlinear equations, variable coefficients, the solution cannot be obtained exactly, see for example

  • The case of zero boundary conditions and constant coefficients has been investigated in Canosa and

  • The first term outer solution and (5.2) reduce to the ones given in Canose and Cole (4) when the coefficient f(x) m 1 and the boundary conditions are zero

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Summary

INTRODUCTION

Many of the problems occurlng in physics, engineering and applied mathematics contain a small parameter, and due to difficulties such as nonlinear equations, variable coefficients, the solution cannot be obtained exactly, see for example. The problem arises in connection with the distribution of the energy released in a nuclear power reactor as a result of a power excursion; r2 (x) is the spacedependent perturbation in the neutron multiplication of a reactor, and I) and (1.2) give the distribution of the energy release from the start of the perturbation till the neutron population again becomes zero, see Ergen (3). Let the maximum value of the solution occur at x c, y(c) M, y’(c) O, y"(c) < 0. Note that if both r2 and f are constant, (2.2) implies that y cannot have any relative minimum. 4. ASYMPTOTIC SOLUTION FOR p(x) 1 AND n IN GENERAL. Substituting it into (4.1), the functions Y. (x) can be determined recursively

The first two terms are given by
Since d

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