Question

Most of practical problems in engineering involve functions of several independent variables as thermal, strain and stress are multidimensional and transient such Two-point backward first order derivative is given Two-point central difference is given by Two-point forward difference is given by Three-point Second order partial derivative central difference is given by The second-order mixed four-point central finite difference is given by (x Convert the boundaries derivatives to second accuracy scheme The vorticity is given by The shear stress is given by

Answer 1

Soluation Given Oat and duldy aye 4hn q9 The Secon d Para desivatve 3udy'calevlule Then 2 J-yi The Second miled dei ivative 3un s Jven y- yi

5535- Chvee -Pon8-oid -nt diferente foimola Con be y-yi a 0.5 -3. 36 443 51 ha three -Poin o ditlernce fomule Can be aul I-yi

3 -3.250 4.361-4 4 123 1O 쿄。 30 tlu) 20 30 SO 6o ID 30 40