Construction of General Implicit-Block Method with Three-Points for Solving Seventh-Order Ordinary Differential Equations

In order to solve general seventh-order ordinary differential equations (ODEs), this study will develop an implicit block method with three points of the form y(7)(ξ)=f(ξ,y(ξ),y′(ξ),y″(ξ),y‴(ξ),y(4)(ξ),y(5)(ξ),y(6)(ξ)) directly. The Hermite interpolation in (GIBM3P) has been derived initial value problems (IVPs) using basic functions interpolating polynomials. A multi-step is constructed be suitable numerical approximation at points. However, construction new presented while results implementations are used prove efficiency and accuracy proposed which compared RK RKM methods together analytical method. We established characteristics method, including zero-stability. Applications various IVP also discussed, outcomes very encouraging for suggested approach. GIBM3P yields more accurate solutions test than existing good agreement solutions.