Advanced Linear Algebra: Session-#2

Advanced Linear Algebra: Session-#2 در جلسه دوم جبر خطی پیشرفته، عمدتا به پاسخ دو سئوال کلیدی زیر پرداخته شد. Why should we study numerical methods such as FDM, FEM, FVM, DQM, etc? در کنار سئوال فوق، سئوال دیگری به شرح ذیل نیز قابل طرح خواهد بود. Are there any other alternatives? در غیاب توسل به روشهای عددی، چاره‌ای جز توسل به روشهای زیر قابل تصور نخواهد بود. Analytical methods; Experimental or physical methods; Analytical methods cannot be implemented due to complexity in one and/ or more of the following issues: Complexity in problem geometry (I. e., Physical or computational domain) Spatial and temporal distribution of forcing function (i. e., Source and sink) Nonlineariry, discontinuity, Spatial and temporal variability due to material properties; Nonlineariry in the governing equations; Complicated initial and boundary conditions; Nonlineariry due to flow regime Experimental or physical methods cannot be used to investigate the impact of the following factors: Complexity in problem geometry (I. e., Physical or computational domain) Spatial and temporal distribution of forcing function (i. e., Source and sink) Nonlineariry, discontinuity, Spatial and temporal variability due to material properties; These methods are time-consuming, labor-intensive, and not cost-effective Numerical methods can incorporate all relevant features in a mathematical model of a physical system because of power of numerical methods and electronic computations. By recurring to numerical methods, one can acquire insight for interpreting the results obtained from ready-made computer code Numerical methods are particularly useful to address "what if scenarios" in a meaningful, cost-effective, time efficient manner.

• #تحصیلات_و_یادگیری
• #analytical_methods
• #numerical_methods
• #experimental_methods