000153662 001__ 153662
000153662 005__ 20251017144606.0
000153662 0247_ $$2doi$$a10.1016/j.apnum.2025.04.007
000153662 0248_ $$2sideral$$a143805
000153662 037__ $$aART-2025-143805
000153662 041__ $$aeng
000153662 100__ $$aJay, Laurent O.
000153662 245__ $$aAnalysis of starting approximations for implicit Runge-Kutta methods applied to ODEs based on the reverse method
000153662 260__ $$c2025
000153662 5203_ $$aWe consider the application of -stage implicit Runge-Kutta methods to ordinary differential equations (ODEs). We consider starting approximations based on values from the previous step to obtain an accurate initial guess for the internal stages of the current step. To simplify the analysis of those starting approximations we compare the expansions of the starting approximation and of the exact value of the internal stages at the initial value of the current step and not at the initial value −1 of the previous step. In particular, for the starting approximation we make use of the
expansion of the reverse IRK method from the initial value of the current step with a negative step size. This simplifies considerably the expression of the order conditions. As a consequence
it allows us to give more general and precise statements about the existence and uniqueness of a starting approximation of a given order for IRK methods satisfying the simplifying assumptions
() and (). In particular we show under certain assumptions the nonexistence of starting approximations of order + 1 for the type of starting approximations considered.
000153662 540__ $$9info:eu-repo/semantics/closedAccess$$aby-nc-nd$$uhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
000153662 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000153662 700__ $$0(orcid)0000-0001-6120-4427$$aMontijano, Juan I.$$uUniversidad de Zaragoza
000153662 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000153662 773__ $$g215 (2025), 1-14$$pAppl. numer. math.$$tAPPLIED NUMERICAL MATHEMATICS$$x0168-9274
000153662 8564_ $$s853327$$uhttps://zaguan.unizar.es/record/153662/files/texto_completo.pdf$$yVersión publicada$$zinfo:eu-repo/date/embargoEnd/2027-04-15
000153662 8564_ $$s1574441$$uhttps://zaguan.unizar.es/record/153662/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada$$zinfo:eu-repo/date/embargoEnd/2027-04-15
000153662 909CO $$ooai:zaguan.unizar.es:153662$$particulos$$pdriver
000153662 951__ $$a2025-10-17-14:15:23
000153662 980__ $$aARTICLE