An accurate method for the numerical solution of fourth order boundary value problem by galerkin method with cubic B-splines as basis functions along with equidistribution of error principle

Fourth order two-point Boundary Value Problems (BVP) usually arise in various fields of science and engineering. In this article, cubic B-splines were utilised as basis functions for solving a fourth-order BVP by the Galerkin method and we have aimed to reduce the upper bound of the error of the numerical solutions obtained with the help of equidistribution of error principle (EDEP). Redefinition of basis functions was implemented to the initially chosen basis functions so that they vanish at all the Dirichlet boundary conditions. On applying the EDEP, the error is equidistributed in each sub-interval of the space variable domain. The proposed method was applied to several linear and non-linear BVPs. The non-linear BVPs were reduced to a sequence of linear BVPs using the concept of quasilinearization. The numerical results obtained are presented in the form of maximum absolute errors without and with applying EDEP, validating the proficiency and precision of the proposed method.