This paper aims to develop a novel third derivative block method with two hybrid points for the direct approximation of third-order Initial Value Problems (IVP). The hybrid points, and , used for the development of the schemes are selected such that they lie in the interval . These derived hybrid schemes are implemented in a block form on some third-order IVPs. The properties of the proposed method including convergence, order, and zero-stability are established. Application of the derived block method on test problems confirms the superiority of the method when compared to exact solutions and existing methods. The numerical results show that the proposed method effectively integrates the third-order Initial Value Problems directly.
Key words: Block method, Differential Equations, Hybrid points, Initial Value Problems, Third-order.
|
