Computational Complexity Analysis of Developing Block Methods for Solving Second Order Ordinary Differential Equations using Numerical Integration, Collocation and Linear Block Approach

摘要

This study presents three approaches for developing block methods for solving second order ODEs. These approaches include the conventional numerical integration and collocation approaches while in addition, considering a new approach called the linear block approach. A sample two-step block method is developed using the two conventional approaches and from the general form taken by the resulting block method, the linear block approach is adopted to directly obtain the block method. To investigate the rigour involved in adopted these approaches, the computational complexity analysis is investigated and it is observed that the new linear block approach is most suitable for developing block methods.