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By introducing a variable substitution we transform the two-point boundary value problem of a third-order ordinary differential equation into a system of two second-order ordinary differential equations. We discretize this order-reduced system of ordinary differential equations by both sinc-collocation and sinc-Galerkin methods, and average these two discretized linear systems to obtain the target system of linear equations. We prove that the discrete solution resulting from the linear system converges exponentially to the true solution of the order-reduced system of ordinary differential equations. The coefficient matrix of the linear system is of block two-by-two structure and each of its blocks is a combination of Toeplit

Topics:
third-order ordinary differential equation, order reduction, sinc-collocation

Year: 2012

OAI identifier:
oai:CiteSeerX.psu:10.1.1.414.2008

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CiteSeerX

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