Block hybrid method using the operational matrices of Bernstein polynomial for the solution of third order ordinary differential equations

Abstract

In this paper, we have developed block method using collocation and interpolation of Bernstein Polynomial  operational matrices to approximate third-order ordinary differential equations (ODEs). The solution give a system  of non linear equations which is solved to give a continuous hybrid linear multistep method. The continuous hybrid  linear multistep method is solved for the independent solutions to give a continuous hybrid block method which is  then evaluated at some off-grid points to give a discrete block method. The basic properties of the discrete block  were investigated and found to be zero stable, consistent and convergent. The derived scheme was tested on some  numerical examples and was found to give better approximation than the existing methods in the literature.