Abstract
In this work, a fourth order ODE of the form is transformed into a system of differential equations that is suitable for solution by means of Numerov method. The obtained solutions are compared with the exact solutions, and are shown to be very effective in solving both initial and boundary value problems in ordinary differential equations.
Highlights
A most preferred method in industry and other applications obtained via the Numerov method, which requires less for numerically solving ordinary differential equations computational complexity, thereby being easier to program
When the differential equation does not include a multistep method (LMM), is a numerical method for solving first order term, the Numerov method comes to mind, as it is second order ordinary differential equations wherein the more accurate than the RK4 by an order
In order to verify numerically whether the proposed schemes are effective, the computations of the approximate numerical solutions of the two fourth order initial and boundary value problems of ordinary differential equations presented in Examples 1 and 2 are implemented using Maple 2019 software package and the results are presented in Tables 1 and 2
Summary
A most preferred method in industry and other applications obtained via the Numerov method, which requires less for numerically solving ordinary differential equations computational complexity, thereby being easier to program. Tsitouras and Simos (2018) proposed a new family of effectively nine stages, ninth-order hybrid explicit Numerov-type methods for solving some special second order initial value problem. Two kinds of interpolants were provided: (i) a three-step interpolation based on all available data at mesh points and (ii) a local interpolant (i.e. two steps) that is constructed after solving scaled equations of condition Application of these interpolants in a set of tests produced global errors of the same magnitude with the underlying method. Simos and Tsitouras (2020) proposed a new low cost two-step hybrid Numerov-type method for solving inhomogeneous linear initial value problems with constant coefficients. By solving a special set of order conditions, it became possible to save one stage (function evaluation) per step for this type of problems when compared with the best existed methods. A linear multistep method is convergent if and only if it is stable and consistent
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
