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Solve the heat equation ut = 10uct for a rod of length 1 with both ends...
Solve the heat equation ut = for all time (zero Neumann boundary conditions), if the initial...
Solve the heat equation ut = for all time (zero Neumann boundary conditions), if the initial temperature is given by (ax)xsin TX. First, formulate the mathematical problem and complete the three steps as described 10uforarod of length 1 with both ends insulated Mathematical Formulation Step 1 Derive an expression for all nontrivial product (separated) solutions including an eigenvalue problem satisfying the boundary conditions Step 2: Solve the eigenvalue problem Step 3: Use the superposition principle and Fourier series to find...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0 < x < 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t>0; I. C.: u(x,0) = 12 + 5cos (6x) – 4cos(21x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann,...
2. Consider the 1D heat equation in a rod of length with diffusion constant Suppose the left endp...
PDE. Please show all steps in detail.
2. Consider the 1D heat equation in a rod of length with diffusion constant Suppose the left endpoint is convecting (in obedience to Newton's Law of Cooling with proportionality constant K-1) with an outside medium which is 5000. while the right endpoint is insulated. The initial temperature distribution in the rod is given by f(a)- 2000 -0.65 300, 0<
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t)...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Ut; 0<x< 6; t> 0; B.C.: 4x(0,t) = 0; uz(6,t) = 0; t> 0; 1. C.: 4(x,0) = 12 + Scos (6x) – 4cos(27x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.:u,(0,t) = 0; ux(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos ( x) – 4cos(27x); 0<x< 6 (a) Whent 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or mixed...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut 0<x< 6; t> 0; B.C.: 4x(0,t) = 0; uz (6,t) = 0; t> 0; 1.C. : u(x,0) = 12 + scos (x) – 4cos(2x); 0 < x < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Ut; 0<x< 6; t> 0; B.C. : Ux(0,t) = 0; Ux(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos (x) – 4cos(21x); 0 < X < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t)...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos (x) – 4cos(27x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,t)...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.: Ux(0,t) = 0; Ux(6,t) = 0; t> 0; 1.C.: u(x,0) = 12 + Scos (x) – 4cos(21x); 0 < x < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet,...
Objective: Solve the wave equation numerically using finite difference methods with both dirichle...
Need help solving it using matlab with for loop
Objective: Solve the wave equation numerically using finite difference methods with both dirichlet and neumann conditions. Consider the wave equation for a string with fixed ends, L=1. lu lu Initial conditions. To make the string behave like a plucked guitar string, use a triangual initial condition. For x less than or equal to 0.5, set u(x, t 0) = 2HX and for x greater than 0.5, use u(x, t = 0)...
Solve the heat equation ut = for all time (zero Neumann boundary conditions), if the initial temperature is given by (ax)xsin TX. First, formulate the mathematical problem and complete the three steps as described 10uforarod of length 1 with both ends insulated Mathematical Formulation Step 1 Derive an expression for all nontrivial product (separated) solutions including an eigenvalue problem satisfying the boundary conditions Step 2: Solve the eigenvalue problem Step 3: Use the superposition principle and Fourier series to find...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0 < x < 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t>0; I. C.: u(x,0) = 12 + 5cos (6x) – 4cos(21x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann,...
PDE. Please show all steps in detail.
2. Consider the 1D heat equation in a rod of length with diffusion constant Suppose the left endpoint is convecting (in obedience to Newton's Law of Cooling with proportionality constant K-1) with an outside medium which is 5000. while the right endpoint is insulated. The initial temperature distribution in the rod is given by f(a)- 2000 -0.65 300, 0<
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Ut; 0<x< 6; t> 0; B.C.: 4x(0,t) = 0; uz(6,t) = 0; t> 0; 1. C.: 4(x,0) = 12 + Scos (6x) – 4cos(27x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.:u,(0,t) = 0; ux(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos ( x) – 4cos(27x); 0<x< 6 (a) Whent 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or mixed...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut 0<x< 6; t> 0; B.C.: 4x(0,t) = 0; uz (6,t) = 0; t> 0; 1.C. : u(x,0) = 12 + scos (x) – 4cos(2x); 0 < x < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = Ut; 0<x< 6; t> 0; B.C. : Ux(0,t) = 0; Ux(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos (x) – 4cos(21x); 0 < X < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos (x) – 4cos(27x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or...
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.: Ux(0,t) = 0; Ux(6,t) = 0; t> 0; 1.C.: u(x,0) = 12 + Scos (x) – 4cos(21x); 0 < x < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet,...
Need help solving it using matlab with for loop
Objective: Solve the wave equation numerically using finite difference methods with both dirichlet and neumann conditions. Consider the wave equation for a string with fixed ends, L=1. lu lu Initial conditions. To make the string behave like a plucked guitar string, use a triangual initial condition. For x less than or equal to 0.5, set u(x, t 0) = 2HX and for x greater than 0.5, use u(x, t = 0)...
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