Non-polynomial splines approach to the solution of sixth-order boundary-value problems. (English) Zbl 1130.65077

Siraj-ul-Islam; Tirmizi, Ikram A.; Fazal-I-Haq; Khan, M. Azam

Appl. Math. Comput. 195, No. 1, 270-284 (2008).

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:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
34B05	Linear boundary value problems for ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations

Keywords:

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

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