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...Chamchuri journal of mathematics volume http www math sc chula ac th cjm modified finite integration method by using legendre polynomials for solving linear ordinary differential equations tanongsak sahakitchatchawan ratinan boonklurb and sirirat singhun received april revised may accepted june abstract in this paper we construct a numerical procedure which is called the polynomial that define solution as combination use zeros computational grid points implement with several examples to demonstrate accuracy our methodcomparingtothefinitedifference traditional methods their analytical solutions keywords subject classification l n introduction usually can explain phenomina occuring sciences engineering economy however under various boundary condi tions real problem configuration it very difficult these corresponding author be solved ease diffi culty play an important role finding approximate actually there are many available such fi nite difference fdm element fem bem etc see wen et al l...