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Solving semi-linear stiff neutral equations by implicit–explicit Runge-Kutta methods

In this paper, for solving semi-linear stiff neutral equations, a class of extended implicit–explicit Runge-Kutta (EIERK) methods are suggested. Under some suitable conditions, it is shown that an EIERK method is convergent of order one or two. The presented numerical examples further verify the theoretical results and effectiveness of the methods. A comparison with the adapted fully implicit Runge-Kutta methods shows that EIERK methods possess the higher computational efficiency.