ABSTRACT
Inordertoimprovetheapproximatesolutions,wecanaddmoretermsto thepreviouslyselectedtrialfunction.Forexample,anothertrialfunctionisu= a 1x(1-x)+a 2 x2(1-x).Thistrialfunctionhastwounknownconstantstobe determined.Computationoftheresidualusingthepresenttrialfunctionyields
(2.1.7)
vVeneedthesamenumberoftestfunctionsasthatofunknownconstantssothatthe constantscanbedeterminedproperly.Table2.1.2summarizeshowtodeterminetest functionsforachosentrialfunctionwhichhasnunknowncoefficients.Application ofTable2.1.2tothepresenttrialfunctionresultsinthefollowingtestfunctionsfor eachmethod.
