STABILITY AND CONVERGENCE OF STIFF SEMILINEAR SYSTEMS BY USING RUNGE-KUTTA METHOD
Abstract
We consider two assumptions on the relative variation of the matrix J ?t?and show that for
each of them there is a family of implicit Runge–Kutta methods that is suitable for the numerical integration of the corresponding stiff semilinear systems, i.e. the methods of the family are stable, convergent and the stage equations possess a unique solution. The conditions on the coefficients of a method to belong to these families turn out to be essentially weaker than the usual algebraic stability condition which appears in connection with the B-stability and convergence for stiff nonlinear systems. Thus there are important RK methods which are not algebraically stable but, according to our theory, they are suitable for the numerical integration of semi linear problems
Author
Dr. M. NALINI
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