Quadratic non-polynomial spline approach to the solution of a system of second-order boundary-value problems. (English) Zbl 1100.65067

Siraj-Ul-Islam; Noor, Muhammad Aslam; Tirmizi, Ikram A.; Khan, Muhammad Azam

Appl. Math. Comput. 179, No. 1, 153-160 (2006).

Summary: A quadratic non-polynomial spline functions based method is developed to find approximations solution to a system of second-order boundary-value problems associated with obstacle, unilateral, and contact problems. The present approach has less computational cost and gives better approximations than those produced by other collocation, finite-difference and spline methods. Convergence analysis of the method is discussed. A numerical example is given to illustrate practical usefulness of the new method.

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
34B05	Linear boundary value problems for ordinary differential equations
65L60	Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations
74M15	Contact in solid mechanics
65L12	Finite difference and finite volume methods for ordinary differential equations

Keywords:

non-polynomial splines; quadratic spline functions; finite-difference methods; obstacle problems; boundary-value problems; comparison of methods; contact problems; collocation; finite-difference; convergence; numerical example

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