A new type of singly-implicit Runge-Kutta method
نویسندگان
چکیده
Implicit Runge-Kutta methods are considered which combine the single-implicitness or diagonal-implicitness property with a zero first row in the coefficient matrix. Acceptable stability for stiff problems is retained by requiring the last stage of a step to be identical to the output value. This requirement, which corresponds to the FSAL property for explicit Runge-Kutta methods, allows the method to have one less SIRK stage to achieve a specific stage order. Examples are given of DIRK, SIRK as well as DESI methods modified in this way. Methods are also proposed which have less than the full stage-order compared with the overall order of the method.
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