GENERALISED SECOND DERIVATIVE MONO IMPLICIT RUNGE-KUTTA METHODS FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS BY Afolabi Gabriel ARIWAYO
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Abstract
ABSTRACT
Numerical schemes for the integration of stiff initial value problems are required to
possess wide region of absolute stability which include the entire left of the complex
plane. Numerical schemes that are explicit usually do not attain the requirement for
integration of stiff initial value problems. In this study, implicit second derivative RungeKutta methods are constructed for the integration of stiff initial value problems.
A family of generalised second derivative mono-implicit Runge-Kutta (GSDMIRK)
method is derived using the method of Tailor series expansion.
The proposed GSDMIRK methods are 𝐴-stable for stage 𝑠=3 𝑎𝑛𝑑 4 and 𝐴(∝)-stable for
𝑠=5 𝑎𝑛𝑑 6. Numerical experiments show that the GSDMIRK methods perform better
when compared to some numerical algorithms in the literature.
Numerical schemes for the integration of stiff initial value problems are required to
possess wide region of absolute stability which include the entire left of the complex
plane. Numerical schemes that are explicit usually do not attain the requirement for
integration of stiff initial value problems. In this study, implicit second derivative RungeKutta methods are constructed for the integration of stiff initial value problems.
A family of generalised second derivative mono-implicit Runge-Kutta (GSDMIRK)
method is derived using the method of Tailor series expansion.
The proposed GSDMIRK methods are 𝐴-stable for stage 𝑠=3 𝑎𝑛𝑑 4 and 𝐴(∝)-stable for
𝑠=5 𝑎𝑛𝑑 6. Numerical experiments show that the GSDMIRK methods perform better
when compared to some numerical algorithms in the literature.
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