On a Class of Implicit Runge-Kutta Procedures

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Abstract
Recently the author has developed a new class of A-stable implicit Runge-Kutta procedures which require the solution of just one system of algebraic equations at each time step rather than the much larger system which has to be solved with most conventional implicit Runge-Kutta procedures. In the present paper a more systematic study of this general class is made and in particular the problems of obtaining exponentially fitted A-stable schemes suitable for the numerical solution of stiff systems of ordinary differential equations and of obtaining estimates for the local truncation error are considered.

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