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5. Find a solution u(x, t) of the following problem utt 0 u(0, t) — и(2,...
3. Finish the following problem we discussed in class today: Utt - и(х, 0) — 0,...
3. Finish the following problem we discussed in class today: Utt - и(х, 0) — 0, и (х, 0) — е-1e1 5 and then plot u(r, 5) for (a) Choose t do it 10 < x < 10. Use a program to (b) Try to figure out what happens as t -» o0, that is find lim u(r, t) t->oo
3. Finish the following problem we discussed in class today: Utt - и(х, 0) — 0, и (х, 0) —...
5. Find a solution u(x,t) of the following problem Ute = 2uz, 0< x < 2 u(0, t) u(2, t) = 0 u(x, 0) = 0, u(x,...
5. Find a solution u(x,t) of the following problem Ute = 2uz, 0< x < 2 u(0, t) u(2, t) = 0 u(x, 0) = 0, u(x, 0) = sin Tx - 2 sin 3ra .
5. Find a solution u(x,t) of the following problem Ute = 2uz, 0
9. Solve the wave problem: 0 < x < T, t> 0; Utt: t2 0; u(T,...
9. Solve the wave problem: 0 < x < T, t> 0; Utt: t2 0; u(T, t) = 0, u(0, t) = 0, 0 SST. u(x,0) = sin(10r), u(x, 0) = sin(4æ) + 2 sin(6x), Answer: sin(10r) sin(10t). 10 sin(4r) cos(4t) + 2 sin(6x) cos(6t) + u(x, t) =
3. (20 pts). Find the solution to the vibrating-string problem: utt u(0,t) u(L,t) u2,0) 2,0) =...
3. (20 pts). Find the solution to the vibrating-string problem: utt u(0,t) u(L,t) u2,0) 2,0) = 0 = 0 2 sin(27/L) + sin(31/L) sin(72/L) 0<<L, 0<t< 0<t< oo 0<t< 0<r<L 0<r<L
5. Solve the heat equation x< T, t > 0 5ихх — бих, и(п,t) — 0 sin (x) 0 и(0, t) и (х,0) t 0 0 x T 5. Solve t...
5. Solve the heat equation x< T, t > 0 5ихх — бих, и(п,t) — 0 sin (x) 0 и(0, t) и (х,0) t 0 0 x T
5. Solve the heat equation x 0 5ихх — бих, и(п,t) — 0 sin (x) 0 и(0, t) и (х,0) t 0 0 x T
Let u(x, t) be the solution to utt = 9uxx for 0 ≤ x ≤ 2...
Let u(x, t) be the solution to utt = 9uxx for 0 ≤ x ≤ 2 and t ≥ 0, where: u(0, t) = 0, u(2, t) = 0, and u(x, 0) = f(x) = 1 − |x − 1|. Use D’Alembert’s solution to find u(1, 0.1) and u(1, 0.8). Be careful to consider that D’Alembert’s solution uses the odd periodic extension of f(x).
5. Consider the following IBVP (initial boundary value problem utt - Curr = 0, 0<x<1, t>0,...
5. Consider the following IBVP (initial boundary value problem utt - Curr = 0, 0<x<1, t>0, with boundary conditions u(0,t) = u(1, t) = 0, > 0 and initial conditions (7,0) = x(1 – 2), 14(2,0) = 0, 0<x< 1. Use separation of variables method to find an infinite series solution of this problem. Do a complete calculation for this problem.
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t)...
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t) 2, u(1, t) = 4 и (х, 0) — 2(1 — х). where s(t) describes the source term (a) Find a series solution for u(x, t) with s(t) = e"1. (b) What is the convergence criteria for the transient extension function if s(t) = 0.
Problem 4: Consider the following problem for the heat equation (1)...
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t)...
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t) 2, u(1, t) = 4 и (х, 0) — 2(1 — х). where s(t) describes the source term (a) Find a series solution for u(x, t) with s(t) = e"1. (b) What is the convergence criteria for the transient extension function if s(t) = 0.
Problem 4: Consider the following problem for the heat equation (1)...
Would like the full steps to get to the answer. Thank you. 6. Find a solution u(x, t) of the following problem 9u 4 0 U...
Would like the full steps to get to the answer. Thank you.
6. Find a solution u(x, t) of the following problem 9u 4 0 Utt u(0, t) u(4, t) 0 0 x2 2 4 ut(r, 0) 0 u(r, 0) 4
6. Find a solution u(x, t) of the following problem 9u 4 0 Utt u(0, t) u(4, t) 0 0 x2 2 4 ut(r, 0) 0 u(r, 0) 4
3. Finish the following problem we discussed in class today: Utt - и(х, 0) — 0, и (х, 0) — е-1e1 5 and then plot u(r, 5) for (a) Choose t do it 10 < x < 10. Use a program to (b) Try to figure out what happens as t -» o0, that is find lim u(r, t) t->oo
3. Finish the following problem we discussed in class today: Utt - и(х, 0) — 0, и (х, 0) —...
5. Find a solution u(x,t) of the following problem Ute = 2uz, 0< x < 2 u(0, t) u(2, t) = 0 u(x, 0) = 0, u(x, 0) = sin Tx - 2 sin 3ra .
5. Find a solution u(x,t) of the following problem Ute = 2uz, 0
9. Solve the wave problem: 0 < x < T, t> 0; Utt: t2 0; u(T, t) = 0, u(0, t) = 0, 0 SST. u(x,0) = sin(10r), u(x, 0) = sin(4æ) + 2 sin(6x), Answer: sin(10r) sin(10t). 10 sin(4r) cos(4t) + 2 sin(6x) cos(6t) + u(x, t) =
3. (20 pts). Find the solution to the vibrating-string problem: utt u(0,t) u(L,t) u2,0) 2,0) = 0 = 0 2 sin(27/L) + sin(31/L) sin(72/L) 0<<L, 0<t< 0<t< oo 0<t< 0<r<L 0<r<L
5. Solve the heat equation x< T, t > 0 5ихх — бих, и(п,t) — 0 sin (x) 0 и(0, t) и (х,0) t 0 0 x T
5. Solve the heat equation x 0 5ихх — бих, и(п,t) — 0 sin (x) 0 и(0, t) и (х,0) t 0 0 x T
5. Consider the following IBVP (initial boundary value problem utt - Curr = 0, 0<x<1, t>0, with boundary conditions u(0,t) = u(1, t) = 0, > 0 and initial conditions (7,0) = x(1 – 2), 14(2,0) = 0, 0<x< 1. Use separation of variables method to find an infinite series solution of this problem. Do a complete calculation for this problem.
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t) 2, u(1, t) = 4 и (х, 0) — 2(1 — х). where s(t) describes the source term (a) Find a series solution for u(x, t) with s(t) = e"1. (b) What is the convergence criteria for the transient extension function if s(t) = 0.
Problem 4: Consider the following problem for the heat equation (1)...
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t) 2, u(1, t) = 4 и (х, 0) — 2(1 — х). where s(t) describes the source term (a) Find a series solution for u(x, t) with s(t) = e"1. (b) What is the convergence criteria for the transient extension function if s(t) = 0.
Problem 4: Consider the following problem for the heat equation (1)...
Would like the full steps to get to the answer. Thank you.
6. Find a solution u(x, t) of the following problem 9u 4 0 Utt u(0, t) u(4, t) 0 0 x2 2 4 ut(r, 0) 0 u(r, 0) 4
6. Find a solution u(x, t) of the following problem 9u 4 0 Utt u(0, t) u(4, t) 0 0 x2 2 4 ut(r, 0) 0 u(r, 0) 4
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