Stability of Runge–Kutta Methods for Stiff Ordinary Differential Equations

1994 ◽  
Vol 31 (4) ◽  
pp. 1147-1168 ◽  
Author(s):  
Roger K. Alexander
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stiff Ordinary Differential Equations ◽  
Runge Kutta

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

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