Abstract
An approximation with spline functions of degree m and deficiency 3 is developed for solving second-order initial-value problems. The stability of the approximate solution is investigated and it is demonstrated that the method is divergent for m ⩾ 7. Convergence is shown for m = 5 and m = 6. Moreover, the method is of order ( m + 1) and error bounds are of the form: [boxV ] S (i) (x)− y i x[boxV ]∞=0 h m + - i ), i=01 m A computational example is presented to illustrate the efficiency of the method.
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