, Volume 44, Issue 2, pp 233-245

Numerical error bounds for fourth order boundary value problems, simultaneous estimation ofu(x) andu″(x)

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For certain nonlinear two-point boundary value problems of the fourth order an estimation theory is developed which yields simultaneous estimates of the solution and its second derivative. Methods for computing numerical error bounds for approximate solutions are described and tested. The theory provides also uniqueness and existence statements. The results can be applied to many problems for which a corresponding theory on two-sided bounds is not suitable.