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Inicio  /  Algorithms  /  Vol: 12 Núm: 1 Par: January (2019)  /  Artículo
ARTÍCULO
TITULO

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

Nizam Ghawadri    
Norazak Senu    
Firas Adel Fawzi    
Fudziah Ismail and Zarina Bibi Ibrahim    

Resumen

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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