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The paper is concerned with the numerical analysis of high-order exponential Rosenbrock-type integrators for large-scale systems of stiff differential equations. The analysis is performed in a semigroup framework of semilinear evolution equations in Banach space. By expanding the errors of the numerical methods in terms of the solution, we further derive new order conditions and thus allows us to construct higher-order methods. A new and more general stiff error analysis is presented to show the converge results for variable step sizes.

SIXTH ORDER EXPLICIT EXPONENTIAL ROSENBROCK-TYPE METHODS FOR SEMILINEAR PARABOLIC PROBLEMS