A Model of a Single Numerical Method for the Integration of Multi-order Ordinary Differential Equations

Computation of numerical methods for the solution of initial value problems (IVPs) of ordinary differential equations (ODEs) has been considered intensely by researchers. However, the use of a single numerical method for the integration of ODEs of different order has not been commonly investigated. This work focused on the development of block model capable of obtaining the numerical solutions of first and second order IVPs, employing Chebyshev polynomials as the basis function. The method is formulated from continuous schemes obtained through collocation and interpolation techniques and applied in a block-by-block manner to numerically integrate first and second order ODEs. The convergence analysis of the method was discussed via zero-stability and consistency. Numerical examples were solved using the developed method and comparisons made with existing methods. The newly developed method has better accuracy in comparison with existing methods