On an Inverse Free Steffensen-Type Method for the Approximation of Stiff Differential Equations

2018 ◽  
Vol 40 (2) ◽  
pp. 119-133
Author(s):  
Sergio Amat ◽  
Sonia Busquier ◽  
Miquel Grau-Sánchez ◽  
M. A. Hernández-Verón ◽  
M. J. Rubio
Keyword(s):  
Differential Equations ◽  
Stiff Differential Equations ◽  
Type Method

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.

A Method for Solving Certain Stiff Differential Equations

1978 ◽  
Vol 34 (4) ◽  
pp. 732-742 ◽  
Author(s):  
Richard J. Clasen ◽  
David Garfinkel ◽  
Norman Z. Shapiro ◽  
Gruia-Catalin Roman
Keyword(s):  
Differential Equations ◽  
Stiff Differential Equations
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