Stability studies of numerical methods for partial differential equations

• Grant number: 12/21478-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2013
• End date: June 30, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Cassio Machiaveli Oishi
• Grantee: Maria Cecília Fonçatti
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil
• Associated research grant: 09/15892-9 - Study of stable and accurate numerical methods for transient flows: improvements, implementations, free surface flow problems and viscoelastic models, AP.JP

Abstract

In this project, it will be investigated numerical stability for solving partial differential equations (PDE) via finite differences. One-dimensional models will be analyzed, for example, advection and heat equations. Based on the matrix method, it will be studied the influence of boundary conditions on the analysis of numerical stability. Initially, the student will investigate the stability of numerical methods for a co-located grid. However, it is intended to extend the stability analysis for a staggered grid. Finally, numerical results will be checked in comparison with the theoretical results obtained from the stability analysis.(AU)