Four step hybrid block method for the direct solution of fourth order ordinary differential equations

‎This paper proposes a direct four-step implicit hybrid block method for directly solving general fourth-order initial value problems of ordinary differential equations‎. ‎In deriving this method‎, ‎the approximate solution in the form of power series is interpolated at four points‎, ‎i.e x_n, ‎x_{n+۱},x_{n+۲},x_{n+۳} while its forth derivative is collocated at all grid points‎, ‎i.e x_n‎,x_{n+\frac{۱}{۴}},‎x_{n+۱}‎ , x_{n+۲}‎, x_{n+\frac{۵}{۲}}‎, x_{n+۳}‎,x_{n+\frac{۷}{۲}} and x_{n+۴} to produce the main continuous schemes‎. ‎In order to verify the applicability of the new method‎, ‎the properties of the new method such as local truncation error‎, ‎zero stability‎, ‎order and convergence are also established‎. ‎The performance of the newly developed method is then compared with the existing methods in terms of error by solving the same test problems‎. ‎The numerical results reveal that the proposed method produces better accuracy than several existing methods when solving the same initial value problems (IVPs) of second order ODEs‎.

کلیدواژه ها:

‎Hybrid block method‎ ، ‎Fourth initial value problem‎ ، ‎Collocation and Interpolation‎ ، ‎Four step