We present a new family of fourth-order splitting methods with positive coefficients especially tailored for the time integration of linear parabolic problems and,in particular,for the time dependent Schrodinger equat...We present a new family of fourth-order splitting methods with positive coefficients especially tailored for the time integration of linear parabolic problems and,in particular,for the time dependent Schrodinger equation,both in real and imaginary time.They are based on the use of a double commutator and a modified processor,and are more efficient than other widely used schemes found in the literature.Moreover,for certain potentials,they achieve order six.Several examples in one,two and three dimensions clearly illustrate the computational advantages of the new schemes.展开更多
基金supported by Ministerio de Ciencia e Innovacion(Spain)through projects PID2019-104927GB-C21 and PID2019-104927GB-C22,MCIN/AEI/10.13039/501100011033,ERDF(“A way of making Europe”)the support of the Conselleria d’Innovacio,Universitats,Ciencia i Societat Digital from the Generalitat Valenciana(Spain)through project CIAICO/2021/180.
文摘We present a new family of fourth-order splitting methods with positive coefficients especially tailored for the time integration of linear parabolic problems and,in particular,for the time dependent Schrodinger equation,both in real and imaginary time.They are based on the use of a double commutator and a modified processor,and are more efficient than other widely used schemes found in the literature.Moreover,for certain potentials,they achieve order six.Several examples in one,two and three dimensions clearly illustrate the computational advantages of the new schemes.
