Four-Point Hybrid Block Method for direct Solution of Third-Order Ordinary Differential Equations

Abstract

 This article presents a four-point hybrid block method for directly solving third-order ordinary differential equations. The method was derived by adopting interpolation and collocation techniques using the Chebyshev polynomial of the first kind as a basis function. The developed method was implemented in block mode. The fundamental properties of the method were investigated to confirm its usability. To evaluate its performance, the method was tested by solving linear and nonlinear initial value problems of third-order ordinary differential equations. The numerical results are compared with existing methods to determine their accuracy. The results show a better accuracy over the existing methods.