Abstract:
The research presented in this dissertation is aimed at the development of family of
numerical solutions of Two Point Boundary-Value Problems (BVP) in all the branches of
engineering sciences with higher precision. In such engineering related boundary-value
problems the boundary conditions are specified at two points.
The core of this dissertation is focused on the development of a new technique based on
quartic non-polynomial spline functions, connecting spline functions values at "mid
knots" for the numerical approximations to engineering BVPs and their corresponding
values of the fourth-order derivatives. This new approach, which is recently being cited,
is so developed that it leads to a family of numerical methods that may be used for
computing approximations to the solution of a system of boundary-value problems of
third and fourth-order associated with contact and sandwich beam problems. This
research work is furthered on the development of a family of higher order numerical
solutions to special non-linear third-order boundary-value problems. It is shown that the
developed family of higher order methods gives better approximations in contrast to the
existing numerical methods. It has further been shown that the existing second, fourth-
order and higher order finite-difference and spline functions based methods become
special cases of our new technique developed at mid knots presented in this dissertation.
Results from the numerical experimentation of renowned problems are also given to
illustrate applicability and efficiency of the newly developed family of numerical
methods.
