Direct solution of initial and boundary value problems of third order ODEs using maximal-order fourth-derivative block method

Improved accuracy has been observed in block methods with the presence of higher derivatives when implemented to solve first order and higher order ordinary differential equations. This improvement in accuracy is as a result of the increased order possessed by the higher derivative block method. In this article, a fourth-derivative block method of maximal-order is introduced to solve third order initial and boundary value problems. The block method possesses convergent properties required for any good numerical method and it is suitable for solving third order ODE models. This is evident in its improved performance over other methods in terms of comparison to the exact solution of the numerical problems considered.