Numerical solution of third-order Robin boundary value problems using diagonally multistep block method

Abstract

Abstract This numerical study exclusively focused on developing a diagonally multistep block method of order five (2DDM5) to get the approximate solution of the third-order Robin boundary value problems directly. The mathematical derivation of the developed 2DDM5 method is by approximating the integrand function with Lagrange interpolation polynomial. The proposed direct integrator scheme was applied to compute numerical solution at two-point concurrently. Shooting technique adapted with the Newtons divided difference interpolation method was implemented throughout the proposed algorithm. The theoretical characteristics of the developed method including the order, consistency, zero-stable and convergence are discussed. The method are tested on four Robin boundary value problems. The numerical results signify that the computational performances of the proposed method is competitive in terms of accuracy and efficiency than the existing method.