On the Derivation of High Order Formulae with Interpolants for Solution of Eight-Point Second Order Ordinary Differential Equations

In this Paper, we extend the idea of collocation of linear multistep methods to develop an eight-point Continuous Block method of order (7,7,7,7,7,7,7,7) T for direct solution of the second order ordinary differential equations.The methods are derived by interpolating the continuous formulation at 𝑥 = 𝑥 𝑛 +𝑗 , 𝑗 = 𝑘 and collocating the first and second derivative of the continuous interpolant at 𝑥 𝑛+𝑗 , 𝑗 = 0,1,2, (𝑘) and 𝑗 = 2, 3, (𝑘) respectively.This approach yielded the multi discrete schemes that form a self-starting uniform order 7 block methods.The convergence analysis of the methods were discussed and the absolute stability regions shown.Two numerical experiments were used to demonstrate the efficiency of the new methods.