A Class of Irrational Linear Multistep Block Method for the Direct Numerical Solution of Third Order Ordinary Differential Equations

This work considers the direct solution of general third order ordinary differential equation by three-step irrational linear multistep method. This method is derived using collocation and interpolation techniques. An irrational three-step method is developed. Taylor series and block methods are used to generate the independent solution at selected points. The properties of the method were also determined. The developed method was applied on general third order ordinary differential equations. And the performance of the numerical results of the method compared favourably with the results of existing authors in the recent literature to test its accuracy and stability.