Efficient Approximate Analytical Methods For Nonlinear Fuzzy Boundary Value Problem

The aim of this paper is to solve the non-linear Two Point Fuzzy Boundary Value Problem (TPFBVP) using the approximate analytical methods. Most fuzzy boundary value problems cannot be solved exactly or analytically. Even if the analytical solutions exist, they may be difficult to evaluate. Therefore approximate analytical methods may be necessary to evaluate the solution. Hence, there is a need to formulate new, efficient, more accurate techniques and this is the focus of this study whereby two approximate analytical methods - Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) are proposed. Fuzzy set theory properties are presented to formulate these methods from crisp domain to fuzzy domain in order to find approximate solutions of nonlinear TPFBVP. The presented algorithms can express the solution as a convergent series form. A numerical comparison of the mean errors is made between the HPM and VIM.  The results show that these methods are reliable and robust. However, the comparison reveals that VIM convergence is quicker and offers a swifter approach over HPM. Hence, VIM is considered a more efficient approach, in particular for nonlinear TPFBVPs