Question

Solve the 1D heat equation $u_t(x, t) = u_{xx}(x, t)$ for $0 < x < 1$, $0 \le t \le 0.1$ by using the explicit F D scheme. The initial and boundary conditions are given as $u(x, 0) = f(x) = \sin(\pi x)$ and $u(0, t) = u(1, t) = 0$. Choose $h = 0.2$, $k = 0.02$.

          Solve the 1D heat equation $u_t(x, t) = u_{xx}(x, t)$ for $0 < x < 1$, $0 \le t \le 0.1$ by using the explicit
F D scheme. The initial and boundary conditions are given as $u(x, 0) = f(x) = \sin(\pi x)$ and
$u(0, t) = u(1, t) = 0$. Choose $h = 0.2$, $k = 0.02$.

Solve the 1D heat equation ut(x, t) = uxx(x, t) for 0 < x < 1, 0 ≤ t ≤ 0.1 by using the explicit
F D scheme. The initial and boundary conditions are given as u(x, 0) = f(x) = sin(π x) and
u(0, t) = u(1, t) = 0. Choose h = 0.2, k = 0.02.

Added by Eileen G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Akash M

12/07/2023

Step 1

2 and k=0.02. This gives us x0=0, x1=0.2, x2=0.4, x3=0.6, x4=0.8, x5=1 for the spatial domain and t0=0, t1=0.02, t2=0.04, t3=0.06, t4=0.08, t5=0.1 for the time domain. Show more…

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Please first solve manually using implicit method then in MATLAB show explicit method Solve the 1D heat equation ut=ut for 0<x<1, 0<t<0.1 by using the explicit FD scheme. The initial and boundary conditions are given as u(x,0) = f(x) = sin(πx) and u(0,t) = u(1,t) = 0. Choose h=0.2, k=0.02.