Find the available Neumann B.C and Mixed B.C of the following 1D laplace eq. And find the solution(answer). Are - 0-...
(1 point) Use eigenvalues and elgenfunction expansion expansion to solve the mixed Dirichlet- Neumann problem for the Laplace equation Au(x, y) = 0 on the rectangle {(x,y) : 0<x<1, 0<y<1} satisfying the BCS ux(0,y) = 0, ux(1, y) = 0, 0 < y < 1 u(x,0) = x, u(x, 1) = 0, 0<x<1 The solution can be written as The u(x, y) = Covo(y)+(x) + .(x).(y) where on is a normalized eigenfunction for "(x) = 10(x) with x(0) = 0...
Find 1d. (LT = Laplace Transforms) use the function: >>pretty(laplace(exp(-a*t)*cos(b*t))) For la – d, find the LTs of the functions by hand, and then use MATLAB to verify the LTs. Include your hand calculations and your MATLAB script for the report. la) 2e-3t + 4te-5t + 6t2 b) 7e-atu(t – 2) c) t(sin(wt)) d) t-e-at
4. Consider the following initial value problem of the 1D wave equation with mixed boundary condition IC: u(z, t = 0) = g(x), ut(z, t = 0) = h(z), BC: u(0, t)0, u(l,t) 0, t>0 0 < x < 1, (a)Use the energy method to show that there is at most one solution for the initial-boundary value problem. (b)Suppose u(x,t)-X()T(t) is a seperable solution. Show that X and T satisfy for some λ E R. Find all the eigenvalues An...
Q3:-Derive the discretization equations for the following differential eq.:- a con +S=0 (roman + dy A):- ad a + ax ax Oy B) d d do I dx dx Use the following continuity eq.:- d(pu) 0 CFD di (oud)
d) Find the Laplace transform of the following function: f (t = 0 to +09) eat dt e) Find the equivalent solution of (d) using MATLAB method(s) (find 2 methods). d) Find the Laplace transform of the following function: f (t = 0 to +09) eat dt e) Find the equivalent solution of (d) using MATLAB method(s) (find 2 methods).
please I need solution as soon as possible Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = uti 0<x< 6; t>0; B.C.: uz (0.t) = 0; ux(6,t) = 0; t> 0; 1. C. :U(x,0) = 12 + 5cos (6x) – 4cos(2x); 0<x<6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (6) Determine whether the boundary...
Please do 1a 1b 1d thanks Assuming x > 0, find the general solution of the following Euler equa- tions. a) x²y" – 3xy' +4y=0 (b)x²y" – 5xy +10y=0 f) 5x2y" + 12. y' + 2y = 0 g) x²y" + xy = 0 1. Assuming 2 > 0, find the general solution of the following Euler equa- tions. a) " - 3xy' + 4y = 0 b) – 5xy +10g = 0 c) 6x²y" + 7xy' - y =...
2-Using the Laplace transform find the solution for the following equation d/ at y(t)) + y(t) = f(t) with initial conditions y(0 b Hint. Convolution Dy(0) = a 2-Using the Laplace transform find the solution for the following equation d/ at y(t)) + y(t) = f(t) with initial conditions y(0 b Hint. Convolution Dy(0) = a
1. Wave equation. Consider the wave equation on the finite interval (0, L) PDE BC where Neumann boundary conditions are specified Physically, with Neumann boundary conditions, u(r, t) could represent the height of a fluid that sloshes between two walls. (a) Find the general Fourier series solution by repeating the derivation from class now considering Neumann instead of Dirichlet boundary conditions. Your final solution should be (b) Consider the following general initial conditions u(x, 0)x) IC IC Derive formulas that...
1. Find the general solution of the Euler eq. 4x’y" +17y=0, x>0.