Two-step Bi-basis Hybrid Block Method for Direct Approximation of Fourth Order Ordinary Differential Equations with Intermediate Bi-intra Points
Abstract:Most recently, higher order problems are being
addressed by decomposing it into system of lower order problems. However, it
was discovered that methods with high order and strong stability were able to
approximate the resulting systems accurately as the problems become unstable in
the region of the new transformation field. This research actually sought for
methods of solution of higher order problems without any need for system
transformation. The method is proposed for the direct solution of fourth order
ordinary differential equations. The fundamental basis is sought from the
combination of Shifted Chebyshev Orthogonal Polynomial and the Hermite
Orthogonal Polynomial, these polynomial functions are then used to obtain the
method using the concept of interpolation and collocation. The proposed method
is found to be consistent and zero-stable, which then implies convergence. From
the numerical results obtained, the efficiency of the method was obtained and
its superiority strength was also established when comparison was made with
existing.