2005•International Journal of Computer MathematicsRequires access

Third-order composite Runge–Kutta method for stiff problems

R. R. Ahmad, Norsuzila Ya’acob

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.

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Key concepts: Runge–Kutta methods, Mathematics, L-stability, Numerical methods for ordinary differential equations, Backward differentiation formula, Ordinary differential equation, Explicit and implicit methods, Numerical stability