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Zbl 1130.65077
Siraj-ul-Islam; Tirmizi, Ikram A.; Fazal-I-Haq; Khan, M.Azam
Non-polynomial splines approach to the solution of sixth-order boundary-value problems. (English)
[J] Appl. Math. Comput. 195, No. 1, 270-284 (2008). ISSN 0096-3003

Summary: Non-polynomial splines, which are equivalent to seven-degree polynomial splines, are used to develop a class of numerical methods for computing approximations to the solution of sixth-order boundary-value problems with two-point boundary conditions. Second-, fourth- and sixth-order convergence is obtained by using standard procedures. It is shown that the present methods give approximations, which are better than those produced by other spline and domain decomposition methods. Numerical examples are given to illustrate the practical usefulness of the new approach.

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)
34B05 Linear boundary value problems of ODE
65L20 Stability of numerical methods for ODE

Keywords: sixth-order BVP; finite-difference methods; non-polynomial splines; convergence; numerical examples

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Zentralblatt MATH Berlin [Germany]