Abstract
To obtain accurate solutions to the time dependent Schrödinger equation, a “product formula” algorithm has been proposed in literature which is both explicit and unconditionally stable. In this paper the accuracy of this algorithm is considered for a few basic problems in mathematical physics, viz. the convection equation and the diffusion equation, in addition to the Schrodinger equation. From a theoretical analysis, which is confirmed by numerical experiments, it is concluded that the product-formula method can indeed produce accurate solutions, but only for small time steps so that the unconditional stability is not of very much use. A comparison is also made with standard finite difference methods, such as leap-frog and Crank-Nicholson.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
