Solve the heat equation by the method of separation of variables 1(1, t) = 0 Эт u,(0, t) = 0, u(x,0) =-2cos( 12. Solve the heat equation by the method of separation of variables 1(1, t) = 0 Эт u...
Solve the heat equation by the method of separation of variables 3π u(x,0)--2cos( x)
ONLY ANSWER 5 and 9. Rating will be provided Exercises for Section 6.2 In Exercises 1-12 use the separation of variables method to solve the heat equation (a, t)auz(t<<l,t>0, subject to the following boundary conditions and the following initial conditions: a = V2, l = 2, u(0,t) = u(2,t)=0, and 5. 20, 0r< 1 0, a(x, 0) = rS 2. 1 1 = π, u(z, 0) = π-z, u(0, t) = uz(mt) = 0. 9. Exercises for Section 6.2 In...
3. Using separation of variables to solve the heat equation, u- kuxx on the interval 0 < x< 1 with boundary conditions ux(0, t) = 0 and ux(1, t) yields the general solution, 1, 0<x < 1/2 0, 1/2 x<1 Determine the coefficients An (n = 0, 1, 2, . . .) when u(x,0) = f(x) = 3. Using separation of variables to solve the heat equation, u- kuxx on the interval 0
3. Using separation of variables to solve the heat equation, u -kuxx on the interval 0x<1 with boundary conditions u(0 and ur(1, t)-0, yields the general solution, u(x, t) =A0 + Σ Ane-k,t cos(nm) (with A, = ㎡π2) 0<x<l/2 0〈x〈1,2 u(x,0)=f(x)-.., , . . .) when u(x,0) = f(x)- Determine the coefficients An (n - 0, 1,2,
1. Solve fully the heat equation problem: Ut = 5ucx u(0,t) = u(1, t) = 0 u(x,0) = x – 23 (Provide all the details of separation of variables as well as the needed Fourier expansions.)
1. Solve the following transient heat equation by separation of variable method. aT At x = 0, BC み_Qo Atx=L, T =To IC: At t = 0, T= 1. Solve the following transient heat equation by separation of variable method. aT At x = 0, BC み_Qo Atx=L, T =To IC: At t = 0, T=
Question 8 [1.5 mark] Solve the heat equation (0,0) = u(2,0) = 0, (u(x,0) - 2 sin (*) - sin(mr) + 4 sin (22) for u = u(x, t): 0,2 x 10,00) +R, using the method of separation of variables.
1. Solve fully the heat equation problem: ut = 5u: u(0,t) = u(1,t) = 0 (3,0) = 2 - 3 (Provide all the details of separation of variables as well as the needed Fourier expansions.)
Page 6 of 6 5. (20 pts) a) Solve the heat equation by the method of separation of variables t>0, 0Sxs1 11T b) Once solution is obtained, find u(0.6,0.002) c) (Bonus) What physical phenomenon is described by this equation? d) (bonus) What physical laws (name at least two) are the used in deriving of this equation? Page 6 of 6 5. (20 pts) a) Solve the heat equation by the method of separation of variables t>0, 0Sxs1 11T b) Once...
1. Solve the following transient heat equation by separation of variable method. ат ах Atx=L, T =To IC: At t = 0, T=T, 1. Solve the following transient heat equation by separation of variable method. ат ах Atx=L, T =To IC: At t = 0, T=T,