Third-order composite Runge–Kutta method for stiff problems

Abstract

The derivation of a composite method for solving stiff ordinary differential equations is discussed. Combination of the harmonic and arithmetic means of the Runge–Kutta formulation has resulted in the introduction of a new formula for the numerical solution of stiff ordinary differential equations. The numerical results and the A-stability of this new formula are examined.

Keywords:

• Runge–Kutta
• Stiff ODEs
• Arithmetic mean
• Harmonic mean
• A-stability