The solution of Differential Equations is an important topic for deliberation among scientists. However, until today, nothing is known on a single-step block method of p-stable for solving third-order Differential Equations (IVPs) whose accuracy is ninth order. This paper focuses on the derivation, analysis, and implementation of the one-step implicit hybrid block method with seven off-step points for direct solution of general third-order ordinary differential equations' initial value problems (IVPs). For the solution of IVPs, the power series functions were utilized as the basis function. To determine the unknown parameters, an approximate solution from the basis function was interpolated at chosen off-grid points. The third derivative of the estimated solution was collocated at all grid and off-grid points to produce a system of linear equations. Consistency, zero stability, convergence, and absolute stability were all evaluated on the method. The numerical results achieved through implementation are quite close to the theoretical solutions and compare well to other novel methods in the literature.

hybrid block method, grid points, off-grid points, 3^rd Order ODE, implicit