Derivation of Embedded Diagonally Implicit Methods for Directly Solving Fourth-order ODEs

Omar Mohammed   Saleh; Firas Adel   Fawzi; Kasim Abas Hussain; Nizam G. Ghawadri

doi:10.30526/37.1.3288

Authors

Omar Mohammed Saleh Department of Mathematics, Faculty of Computer Science and Mathematics, University of Tikrit, Tikrit, Iraq,
Firas Adel Fawzi Department of Mathematics, Faculty of Computer Science and Mathematics, University of Tikrit, Tikrit, Iraq,
Kasim Abas Hussain Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq.
Nizam G. Ghawadri Doctor of Mathematics, Ministry of Education, Jenin, Palestine.

DOI:

https://doi.org/10.30526/37.1.3288

Abstract

EDIRKTO, an Implicit Type Runge-Kutta Method of Diagonally Embedded pairs, is a novel approach presented in the paper that may be used to solve 4th-order ordinary differential equations of the form . There are two pairs of EDIRKTO, with three stages each: EDIRKTO4(3) and EDIRKTO5(4). The derivation techniques of the method indicate that the higher-order pair is more accurate, while the lower-order pair provides superior error estimates. Next, using these pairs as a basis, we developed variable step codes and applied them to a series of -order ODE problems. The numerical outcomes demonstrated how much more effective their approach is in reducing the quantity of function evaluations needed to resolve fourth-order ODE issues.