Abstract
This work aims to clarify and discuss, in a simultaneously accurate and simple way, some relevant issues on the stability and convergence of numerical solutions that are not usually presented in the literature and available for the students in this form. These include stability and physically realistic solutions of unsteady problems, and why the unconditionally stable Crank-Nicolson scheme can lead to nonphysical solutions. Similarities and differences between stability and convergence are highlighted, and it is shown how they can be ensured by the numerical schemes. Many practical problems require underrelaxation for successful convergence, and it is discussed and clarified why and how underrelaxation improves convergence and affects stability. The physical reasons behind the stability criteria required for successful numerical solution of unsteady diffusion problems are presented and discussed.
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.
