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Fourth order two-point boundary value problems; estimates by two-sided bounds. (English) Zbl 0533.34019

The paper is concerned with transforming two-point boundary value problems of the fourth order into problems of the second order, such that known results on two-sided estimates can be applied effectively. The method of transformation is described for problems of the form \[ (au'')''+f(x,u)=0,\quad u(0)=u'(0)=u(1)=u'(1)=0. \] This special case has certain typical difficulties. Generalizations to a series of other problems are straightforward. Numerical examples demonstrate the efficiency of the approach.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
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References:

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