1D heat equation with non-homogenous boundary conditions

Related BrainMass Solutions

• Non homogeneous 1D heat equation

  624667 Non homogeneous 1D heat equation ut = 3uxx + 2, 0 < x < 4, t > 0, u(0,t) = 0, u(4,t) = 0, t = 0 u(x,0) = 5sin2πx,0 < x < 4. (a) Find the steady state solution uE(x) (b) Find an expression for the solution.

• The non-homogeneous heat equation

  Any homogenous heat equation with non-homogenous Dirichlet\Neumann boundary conditions can be easily converted to a non-homogenous heat equation with homogeneous Dirichlet\Neumann boundary conditions.

• 1D heat equation

  with time-dependent boundary values to a simple non-homogeneous equation, and in a special case how to get the steady state and asymptotic behavior

• The 1D heat equation

  241523 The 1D heat equation Please see the attached file for the fully formatted problems.

• One dimensional heat equation

  This is called the "Neuman boundary condition": (1.4) In most cases with Neumann conditions the ends are adiabatically insulated - that is there is no flux through the ends: (1.5) And now we can start solving the homogenous heat equation.

• Steady State Solution

  In that case, first of all we have the heat equation with homogenous boundary conditions. Moreover, we will have v(x)= Px+ Q v(0)= T0 v(a)= T1 Therefore, v(x)= ((T1- T0)/a)x+ T0 (the same as the steady state response).

• Solve the IBVP for the heat equation.

  397035 Solve the IBVP for the heat equation. Please show all steps. Thank you. Solve the IBVP for the heat equation u_t = u_xx, 0 < x < pi, with Neumann boundary conditions u_x(0, t) = 1, u_x(pi, t) = 0, and initial condition u(x, 0) = 0.

• Partial Differential Equations : Eigenvalue Expansion

  only way we can get a non-trivial solution for periodic boundary conditions.

• 1D heat equation with variable diffusivity

  242478 1D Heat Equation with Variable Diffusivity Please provide a detailed solution to the attached problem.