Theexactanalyticmethodwasgivenby[1].Itcanbeusedforarbitraryvariablecoefficientdifferentialequationsandthesolutionobtainedcanhavethesecondorderconvergentprecision.Inthispaper,anewhighprecisionalgorithmisgivenbasedon[1],throughabendingproblemofvariablecross-sectionbeams.Itcanhavethefourthconvergentprecisionwithoutincreasingcomputationwork.Thepresentcomputationmethodisnotonlysimplebutalsofast.Thenumericalexamplesaregivenattheendofthispaperwhichindicatethatthehighconvergentprecisioncanbeobtainedusingonlyafewelements.Thecorrectnessofthetheoryinthispaperisconfirmed.
