Three-step Four-point Optimized Hybrid Block Method for Direct Solution of General Third Order Differential Equations
Asian Research Journal of Mathematics · pp. 25–44 · Published 6 Apr 2023
10.9734/arjom/2023/v19i6664Abstract
This research work considers derivation of three step four point optimized hybrid block method for solving general third order differential equations (odes) without reduction to systems of lower order odes. A combination of power series and exponential function is used as an approximate solution to the general third order ode problems. Continuous linear multistep method is developed by interpolating the basis function at both grid and off-grid points and collocating the differential function at only grid points. The unknown parameters in the system of linear equations arising from the collocation and interpolation functions were determined and the values substituted in the approximate solution to the problem. The required continuous method is obtained after necessary simplification. The derived method is tested and found to be consistent, symmetric and of low error constant. The results obtained showed a better performance than the existing methods in literature under review.
Cited by 2
Ibrahim Mohammed Dibal, Yeak Su Hoe · AppliedMath · 2026
Showing 1 of 2 known citations — external sources report more than can currently be individually listed.
Related research
- Construction of Five-step Continuous Block General Method for the Solution of Ordinary Differential Equations — shares topic coverage
- 3- Point Single Hybrid Block Method (3PSHBM) for Direct Solution of General Second Order Initial Value Problem of Ordinary Differential Equations — shares topic coverage
- Implicit Hybrid Points Approach For Solving General Second Order Ordinary Differential Equations With Initial Values — shares topic coverage
- Study for Uniform Convergence and Power Series — shares topic coverage
- A 2-Step Four-Point Hybrid Linear Multistep Method for Solving Second Order Ordinary Differential Equations Using Taylor’s Series Approach — shares topic coverage
Article metrics
Real usage data collected on this platform.
22
Page views
0
PDF downloads
2
Outbound clicks
2
Citations
Views over time
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
Traffic sources
Referring site, by host.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.