Abstract
A cubic spline function has been applied to the solution of the second-order nonlinear two-point boundary value problems with significant first derivatives. The method obtained involves some parameters. These parameters may be suitably chosen to obtain an oscillation-free solution of the test equation y″ = Ky′, K ⪢ 1. Depending upon the choice of the parameters, methods of order two, three and four may be obtained. The methods have been tested on both linear and nonlinear problems.
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