Abstract:
Subdivision schemes are important for the generation of smooth curves and
surfaces through an iterative process from a finite set of points. The subdivision
schemes have been considered well-regarded in many fields of computational
sciences. In this dissertation, we have used subdivision schemes for the numerical
solution of different types of boundary value problems. In literature three
methods such as spline based methods, finite difference methods and finite element
methods are commonly used to find the numerical solution of boundary
value problems. Subdivision based algorithms for the numerical solution of
second order boundary value problems have also been used in the literature.
In this dissertation, we develop subdivision based collocation algorithms for
the numerical solution of linear and non linear boundary value problems of order
three and four. Subdivision based collocation algorithms for the solution
of second and third order singularly perturbed boundary value problems are
also presented in this dissertation. These algorithms are developed by using basis
functions of subdivision schemes. Convergence analysis of these collocation
algorithms are also discussed. Accuracy and efficiency of the developed algorithms
are shown through comparison with the existing numerical algorithms.
