scholarly journals Stepsize Selection in Explicit Runge-Kutta Methods for Moderately Stiff Problems

2011 ◽  
Vol 02 (06) ◽  
pp. 711-717 ◽  
Author(s):  
Justin Steven Calder Prentice
Keyword(s):  
Stiff Problems ◽  
Runge Kutta ◽  
Stepsize Selection

Construction of Third-Order Diagonal Implicit Runge–Kutta Methods for Stiff Problems

2009 ◽  
Vol 26 (8) ◽  
pp. 080503 ◽  
Author(s):  
Osama Yusuf Ababneh ◽  
Rokiah@rozita Ahmad
Keyword(s):  
Stiff Problems ◽  
Third Order ◽  
Runge Kutta

Explicit Runge–Kutta Methods for Stiff Problems with a Gap in Their Eigenvalue Spectrum

2018 ◽  
Vol 77 (2) ◽  
pp. 1055-1083 ◽  
Author(s):  
Philippe Bocher ◽  
Juan I. Montijano ◽  
Luis Rández ◽  
Marnix Van Daele
Keyword(s):  
Stiff Problems ◽  
Eigenvalue Spectrum ◽  
Runge Kutta

scholarly journals Rational Approximation Method for Stiff Initial Value Problems

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3185
Author(s):  
Artur Karimov ◽  
Denis Butusov ◽  
Valery Andreev  ◽  
Erivelton G. Nepomuceno
Keyword(s):  
Rational Approximation ◽  
Taylor Series ◽  
Approximation Method ◽  
Stiff Problems ◽  
Superior Performance ◽  
Series Method ◽  
Accuracy Order ◽  
Taylor Series Method ◽  
Runge Kutta ◽  
The Right

While purely numerical methods for solving ordinary differential equations (ODE), e.g., Runge–Kutta methods, are easy to implement, solvers that utilize analytical derivations of the right-hand side of the ODE, such as the Taylor series method, outperform them in many cases. Nevertheless, the Taylor series method is not well-suited for stiff problems since it is explicit and not A-stable. In our paper, we present a numerical-analytical method based on the rational approximation of the ODE solution, which is naturally A- and A(α)-stable. We describe the rational approximation method and consider issues of order, stability, and adaptive step control. Finally, through examples, we prove the superior performance of the rational approximation method when solving highly stiff problems, comparing it with the Taylor series and Runge–Kutta methods of the same accuracy order.

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