Mathematicians are researching solutions to resolve many of today's technical challenges. Numerical techniques are used to solve the mathematical models in engineering problems. Many of the mathematical models of engineering problems are expressed in terms of Boundary Value Problems. A finite element method involving collocation method with B-splines as basis functions has been developed to solve fourth order boundary value problems. The fourth order and third order derivative for the dependent variable are approximated by the central differences of second order derivatives. The basis functions are redefined into a new set of basis functions which in number match with the number of collocated points selected in the space variable domain. The proposed method is tested on a linear boundary value problems. Numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.

A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematics