Abstract
A new error bound for any approximate solutionu of the two-point boundary value problemAy:=−(py′)′+qy=f,y(0)=0, y(1)=0, is proposed. This error bound depends on the deviationAu−fjust like the one which is proportional to ‖Au−f‖2, but in the case of Ritz-Galerkin approximations by cubic splines it behaves asymptotically likeh3, whereh is the knot distance, i.e., it is by one order of magnitude better.
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