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.


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