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In this article, the Parker-Sochacki method is extended to solving boundary values of Nth order differential equations. By recasting the problem as a system of constant coefficient polynomial ordinary differential equation, the coefficients of the power series solution is computed iteratively. The closed form solution is obtained by employing Laplace-Padé series summation as an aftertreatment procedure. Application of the new technique to various examples elucidated the accuracy and reliability of the approach. AMS Subject Classification: 65L05, 65L06

IMPROVED PARKER-SOCHACKI METHOD FOR CLOSED FORM SOLUTION OF TWO AND THREE-POINT BOUNDARY VALUE PROBLEMS OF $N$-TH ORDER ODES