A Fourth Order Runge-Kutta Gill Method for the Numerical Solution of Intuitionistic Fuzzy Differential Equations

2018 ◽  
pp. 55-68 ◽  
Author(s):  
B. Ben Amma ◽  
Said Melliani ◽  
L. S. Chadli
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Fourth Order ◽  
Intuitionistic Fuzzy ◽  
Runge Kutta

HISTORY TRACKING ABILITY OF HYBRID SECOND AND FOURTH ORDERS RUNGE-KUTTA IN SOLVING DELAY DIFFERENTIAL EQUATIONS

2017 ◽  
Vol 79 (6) ◽  
Author(s):  
Rui Sih Lim ◽  
Rohanin Ahmad ◽  
Su Hoe Yeak
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Numerical Scheme ◽  
Third Order ◽  
Acceptable Error ◽  
Tracking Ability ◽  
Runge Kutta ◽  
Delay Differential

This paper presents numerical solution for Delay Differential Equations systems to identify frequent discontinuities which occur after and sometimes before the initial solution. The Runge-Kutta methods have been chosen because they are well-established methods and can be modified to handle discontinuities by means of mapping of past values. The state system of the problem is first discretized before the method is applied to find the solution. Our objective is to develop a scheme for solving delay differential equations using hybrid second and fourth order of Runge-Kutta methods. The results have been compared with the result from Matlab routine dde23 which used second and third order of Runge-Kutta methods.  Our numerical scheme is able to successfully handle discontinuities in the system and produces results with acceptable error.

One Step Cosine–Taylorlike Method For Solving Stiff Equations

2012 ◽  
Author(s):  
Rokiah @ Rozita Ahmad ◽  
Nazeeruddin Yaacob
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Explicit Method ◽  
Stiff Ordinary Differential Equations ◽  
One Step ◽  
Runge Kutta ◽  
New Formula ◽  
Better Than

Makalah ini membincangkan penghasilan kaedah tak tersirat bak Cosine–Taylor untuk menyelesaikan persamaan pembezaan biasa kaku. Perumusannya menghasilkan pengenalan kepada satu rumus baru bagi penyelesaian berangka bagi persamaan pembezaan biasa kaku. Kaedah baru ini memerlukan penghitungan tambahan yakni melakukan beberapa terbitan bagi fungsi yang terlibat. Walau bagaimanapun, keputusan yang diperoleh adalah lebih baik berbanding hasil yang didapati apabila menggunakan kaedah tak tersirat Runge–Kutta peringkat–4 dan kaedah tersirat Adam–Bashfiorth–Moulton (ABM). Perbandingan yang dibuat dengan kaedah bak Sine–Taylor menunjukkan kejituan bagi kedua–dua kaedah adalah hampir setara. Kata kunci: Kaedah tak tersirat; persamaan pembezaan biasa kaku; Runge–Kutta; kaedah tersirat; Adam–Bashforth–Moulton; bak Sine–Taylor This paper discusses the derivation of an explicit Cosine–Taylorlike method for solving stiff ordinary differential equations. The formulation has resulted in the introduction of a new formula for the numerical solution of stiff ordinary differential equations. This new method needs an extra work in order to solve a number of differentiations of the function involved. However, the result produced is better than the results from the explicit classical fourth–order Runge–Kutta (RK4) and the implicit Adam–Bashforth–Moulton (ABM) methods. When compared with the previously derived Sine–Taylorlike method, the accuracy for both methods is almost equivalent. Key words: Explicit method; stiff ordinary differential equations; Runge–Kutta; implicit method; Adam–Bashforth–Moulton; Sine–Taylorlike

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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