Direct Solution of General Fourth-Order Ordinary Differential EquationsUsing the Diagonally Implicit Runge-Kutta Method

Authors

  • 1Department of Mathematics, Faculty of Computer Science and Mathematics, University of Tikrit, Tikrit, Iraq
  • 2Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq

DOI:

https://doi.org/10.32792/jeps.v13i1.249

Keywords:

initial value problem, general fourth-order ODEs, implicit Runge-Kuttatype methods

Abstract

The diagonally implicit Runge-Kutta method (DIRKT), fourth-and fifth-order, is developed in this study
to solve general fourth-order ordinary differential equations (ODEs). DIRKTO5 and DIRKTO4,
respectively, are the names of these methods. Both methods consist of three stages. A collection of test
problems were utilized to support the methodologies. The numerical outcomes demonstrated that the
suggested approaches performed better than the implicit Runge-Kutta (RK) methods in terms of precision
and the quantity of the evaluations of function.

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Published

2023-04-10

Issue

Vol. 13 No. 1 (2023): Journal of Education for Pure Science- University of Thi-Qar

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