A sixth‐order improved Runge–Kutta direct method for special third‐order ordinary differential equations

2020 ◽  
Author(s):  
Mukaddes Ökten Turacı ◽  
Merve Özdemir
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Direct Method ◽  
Sixth Order ◽  
Third Order ◽  
Runge Kutta

scholarly journals INTEGRATION FOR SPECIAL THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS USING IMPROVED RUNGE-KUTTA DIRECT METHOD

2015 ◽  
Vol 34 (2) ◽  
pp. 172-179 ◽  
Author(s):  
Kasim Abbas Hussain ◽  
Fudziah Ismail ◽  
Norazak Senu ◽  
Faranak Rabiei ◽  
Rabha Ibrahim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Direct Method ◽  
Third Order ◽  
Runge Kutta

scholarly journals Diagonally Implicit Runge–Kutta Type Method for Directly Solving Special Fourth-Order Ordinary Differential Equations with Ill-Posed Problem of a Beam on Elastic Foundation

Algorithms ◽  
2018 ◽  
Vol 12 (1) ◽  
pp. 10 ◽  
Author(s):  
Nizam Ghawadri ◽  
Norazak Senu ◽  
Firas Adel Fawzi ◽  
Fudziah Ismail ◽  
Zarina Ibrahim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Elastic Foundation ◽  
Fourth Order ◽  
Sixth Order ◽  
Test Problems ◽  
Type Method ◽  
Ill Posed ◽  
Runge Kutta ◽  
Fifth Order

In this study, fifth-order and sixth-order diagonally implicit Runge–Kutta type (DIRKT) techniques for solving fourth-order ordinary differential equations (ODEs) are derived which are denoted as DIRKT5 and DIRKT6, respectively. The first method has three and the another one has four identical nonzero diagonal elements. A set of test problems are applied to validate the methods and numerical results showed that the proposed methods are more efficient in terms of accuracy and number of function evaluations compared to the existing implicit Runge–Kutta (RK) methods.

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