CME261H1 Lecture Notes - Lecture 40: Heat Equation, Euler Method, Taylor Series

• School: UTSG
• Department: Civil and Mineral Engineering
• Course: CME261H1
• Professor: Marianne Hatzopoulou

Document Summary

An found from initial conditions. steady two - dimensional heat problem. Dirichlet problem : temperature u is prescribed on c: heumann, robin problem : rate of temperature change (cid:195) is ::c::: :::"m . problem, dirichlet problem , given b. c. , y) = u ( d , y) - uld , 03=0. , uh , y) = fi ant . sin sinh matt. =2- a - sinh chaba , i fo" f ca) n sin ht . da: 3 solutions. Pdes : a uxx t b day t c uyy = fck , y , u , Ux , uy ) a c - b. For example ) . steady 3d heat flow ( 3. 7+37. Ground water flew . i: humerus for odes. In the euler method , we used taylor expansion , y cath) = y ca) th y ca: humerus h. Ux ( x. y) e ih (ucxthy ) - uh -hey )) from cl) and subtract.