10 Find approximate solution of the following boundary and initial value (,0) 8 problem by using the implicit FDM2)4 u(5,t)0 for u,1 uai. 1.1 At 0.5 10 Find approximate solution of the follo...
4.[10] Find the solution to given initial-boundary value problem: 4uxx = U, 0 < x <TT, t> 0 u(0,t) = 5, u(t, t) = 10, t> 0 u(x,0) = = sin 3x - sin 5x, 0<x<
Find the solution u(a, t) to the initial boundary value problem for the heat equation 4urx te (0, 00), a e (0,5), with initial condition e [0,) e ,5 | 3, u(0, ar) f(ar) = 4, and with boundary conditions ug (t, 0) = 0, un (t, 5) = 0. Find the solution u(a, t) to the initial boundary value problem for the heat equation 4urx te (0, 00), a e (0,5), with initial condition e [0,) e ,5 |...
4. [10] Find the solution to given initial-boundary value problem: 4uxx = ut 0<x<TI, t> 0 u(0,t) = 5, uit, t) = 10, t> 0 u(x,0) = sin 3x - sin 5x, 0<x<T
Let u be the solution to the initial boundary value problem for the Heat Equation u(t, x) 4ut, x) te (0, o0), т€ (0, 3)%; with initial condition 2. f(x) u(0, x) 3 0. and with boundary conditions ди(t, 0) — 0, и(t, 3) — 0. Find the solution u using the expansion u(t, a) "(2)"п (?)"а " п-1 with the normalization conditions Vn (0) 1, wn(0) = 1 a. (3/10) Find the functions wn. with index n > 1....
Let u be the solution to the initial boundary value problem for the Heat Equation, u(t, x)20u(t, x) te (0, oo) те (0, 1); with initial condition , u(0, a) f(x) and with boundary conditions и(t, 0) — 0, и(t, 1) — 0. Find the solution u using the expansion "(т)Чт (?)"а " (1')п 1 with the normalization conditions Vn (0) 1, 1. Wn 2n a (3/10) Find the functions w, with index n 1. b. (3/10) Find the functions...
Let u be the solution to the initial boundary value problem for the Heat Equation au(t,) -48Fu(t,), te (0,oo), z (0,5); with boundary conditions u(t,0) 0, u(t,5) 0, and with initial condition 5 15 15 The solution u of the problem above, with the conventions given in class, has the form with the normalization conditions vn(0)-1, u Find the functions vnwn and the constants cn n(t) wnr) Let u be the solution to the initial boundary value problem for the...
Let u be the solution to the initial boundary value problem for the Heat Equation, Hw29 7.3 HE: Problem 7 Problem Value: 10 point(s). Problem Score: 0%. Attempts Remaining: 17 attempts (10 points) Let u be the solution to the initial boundary value problem for the Heat Equation, Stu(t, x)-46?u(t, x), t E (0, 00), x e (0,5); with initial condition 0 and with boundary conditions Find the solution u using the expansion with the normalization conditions 1 a. (3/10)...
Let u be the solution to the initial boundary value problem for the Heat Equation дли(t, 2) — 4 әғи(t, 2), te (0, o0), те (0,1); with initial condition , u(0, a)f() and with boundary conditions 0. u(t, 0)0 u(t, 1) Find the solution u using the expansion и(t, г) "(2)"т (?)"а " n 1 with the normalization conditions 1 Vn (0) 1, wn 2n a. (3/10) Find the functions wn, with index n> 1. Wn b. (3/10) Find the...
Let u be the solution to the initial boundary value problem for the Heat Equation an(t,r)-301a(t, z), te(0,00), z E (0,3); with initial condition 3 0 and with boundary conditions 6xu(t,0)-0, u(t, 3) 0 Find the solution u using the expansion with the normalization conditions vn (0)-1, wn(0) 1 a. (3/10) Find the functionsw with index n1 b. (3/10) Find the functions vn with index n1 Un c. (4/10) Find the coefficients cn, with index n 1 Let u be...
Let u be the solution to the initial boundary value problem for the Heat Equation, dụı(t, x)-20 11(t, x), IE(0, oo), XE(0,3); with initial condition u(0,x)-f (x), where f(0) 0 andf'(3)0, and with boundary conditions Using separation of variables, the solution of this problem is with the normalization conditions 3 a. (5/10) Find the functions wn, with index n 1. wn(x) = 1 . b. (5/10) Find the functions vn, with index n Let u be the solution to the...