GENERALISED SECOND DERIVATIVE MONO IMPLICIT RUNGE-KUTTA METHODS FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS
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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 Runge
Kutta 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 ��=5 𝑎𝑛𝑑 6. Numerical experiments show that the GSDMIRK methods perform better when compared to some numerical algorithms in the literature.
Kutta 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 ��=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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