Given v (678) = U (,1;8%)*(x",0)de where U (,t;a") = ( 217 )* <im(8=e")°/2nt and 1...
(1 point) Solve the heat problem with non-homogeneous boundary conditions ∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0 u(0,t)=0, u(3,t)=2, t>0,u(0,t)=0, u(3,t)=2, t>0, u(x,0)=23x, 0<x<3.u(x,0)=23x, 0<x<3. Recall that we find h(x)h(x), set v(x,t)=u(x,t)−h(x)v(x,t)=u(x,t)−h(x), solve a heat problem for v(x,t)v(x,t) and write u(x,t)=v(x,t)+h(x)u(x,t)=v(x,t)+h(x). Find h(x)h(x) h(x)=h(x)= The solution u(x,t)u(x,t) can be written as u(x,t)=h(x)+v(x,t),u(x,t)=h(x)+v(x,t), where v(x,t)=∑n=1∞aneλntϕn(x)v(x,t)=∑n=1∞aneλntϕn(x) v(x,t)=∑n=1∞v(x,t)=∑n=1∞ Finally, find limt→∞u(x,t)=limt→∞u(x,t)= Please show all work. (1 point) Solve the heat problem with non-homogeneous boundary conditions au ди (x, t) at (2, t), 0<x<3, t> 0 ar2 u(0,t) = 0, u(3, t) = 2, t>0, u(t,0)...
Problem 4. Solve for the functions u, v, and w, where (1) (∂/∂t + ∂/∂x) u = a, (2) (∂/∂t − ∂/∂x) v = b, and (3) (∂/∂t + 3 ∂/∂x) w = c, where a, b, and c are the functions that you calculated in Problem 3... a=f(x+t)= (x+t)^2+(x+t)+1 b=f(x-2t)= (x-2t)^2+(x-2t)+1 c=f(x-3t)= (x-3t)^2+(x-3t)+1
l, t)4u (x, t), 0<x< L, 0 <t Evaluate u(1.1; 0.3) where u(x, t) u(0, 1)= u(L, t)- 0v1> 0 u(x, 0)= f(x), u,(x, 0)- g(x), 0<x< L L=T al f(x) 3sin 2x, g(x)=-2sin 3x b/ For f(x)-xn-x & g(x)-0, approximate numerically u(x, t) by the first term. L-S c/f(x)=-3sin g(x)- 5 2sin d/ f(x)-0, g()= .3 x +1 approximate numerically u(x, t) by the first term c/ f(x)-2(5-xx, g(x) x+1 3 approximate numerically u(x, t) by the first couple...
ut = Kuzz-cr(z-L) where u = u(x, t) for 0 L and t 0 a(0,t) = 1 (a(L, t) = 1 where к.с > 0 are constants. For all plots in this lab, we will take c-2, к-3. L-1, but L will otherwise be left unspecified We were unable to transcribe this image ut = Kuzz-cr(z-L) where u = u(x, t) for 0 L and t 0 a(0,t) = 1 (a(L, t) = 1 where к.с > 0 are constants....
Mark which statements below are true, using the following: Consider the diffusion problem au Ou u(0, t) = 0, u(L, t) = 50 u(x,0-fx where FER is a constant, forcing term. Any attempt to solve this using separation of variables fails. This is because the PDE is not homogeneous. A more fruitful approach arises from splitting the solution into the sum of two parts, taking into account that all change eventually dies out. That is there is a transient part...
Solve the DE for x(t) given the following DE and volume solution of V(t) then answer the case1 and case 2 questions V(t)=180-100e-0.01t+20e-0.05t Case 1 Let i(t) = e-0.01t and r(t) = e-0.05t Solve for x(t) and plot a graph for x(t) and the function V(t) What is the limiting value of x(t) that is what is x(t) as t goes to infinity. How does the solution vary as a function given the initial conditions of X0=0,...
for the following parabolic PDEs heat equation for one variable d2/dx² u(x,t) = d/dt u(x,t) . Where u(0,t)=0 , u(1,t)=0 , u(x,0)=sinπx . Complete using crank nicolson method . With h=0.2 , k=0.02
Calculate i(t) for t> 0 in the given circuit. Assume A = 35[1 – u(t)] V. + V - 1 F 16 A +1 H 592 The value of i(t) = (A) cos (Ct + Dº)u(t) A where A = C= and D =
Solve u, = 4 for 0 5xs1, given u(0,t) = 0, u,(1,t) = 0, u(x,0)=1. 2 fomu sin 1 Answer: u(x,t) = { e "sin( n +) 7x 0 1 +
(40 pts) 2a. Show that u(z) is the solution to the problem where k(x)-1 for x < 1/2 and k = 2 for x > 1 /2. 2b. Set up the weak form for the differential equation above and the resulting element stiffness and element load vector and calculate the element stiffness matrix and load vector for 4 quadratic elements by using the Gaussian quadrature that is going to exactly calculate the integrals Then set up the global K and...