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Solve the wave equation on the half-line with the Dirichlet boundary condition at x = 0:Utt - c^2uxx = 0, x > 0, t âˆˆ R;u(x,0) = 0, x > 0;Ut(x,0) = sin(x), x > 0;u(0,t) = 0, t âˆˆ R.

Solve the wave equation on the half-line with the Dirichlet boundary co…

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SOLVED:In Exercises 1-4, solve the Dirichlet problem (1)-(2) for the given boundary data. f(x)= 100(1 x) if -1<x<0 100(1-x) if 0<x<1 0 otherwise

SOLVED:In Exercises 1-4, solve the Dirichlet problem (1)-(2) for the gi…

SOLVED:Consider the electrostatic Green functions of Section 1.10 for Dirichlet and Neumann boundary conditions on the surface S bounding the volume V. Apply Green's theorem (1.35) with integration variable 𝐲 and ϕ=G(𝐱, 𝐲), ψ=G(𝐱^', 𝐲). with ∇^2 y G(z, y)=-4 πδ(𝐲-𝐳). Find an expression for the difference [G(𝐱, 𝐱^')-. .G(𝐱^', 𝐱)] in terms of an integral over the boundary surface S. (a) For Dirichlet boundary conditions on the potential and the associated boundary condition on the Green

SOLVED:Consider the electrostatic Green functions of Section 1.10 fo…

SOLVED: Consider the Dirichlet wave problem on the finite interval:Utt - Uxx = 0, for 0 < x < 1,u(x,0) = 2(1 - x^2), u(0,t) = u(1,t) = 0.Find the value of the solution at the point x = 8/3. Notice that in this problem c = 1, so the period of the extended data will be 2L = 2(1) = 2.Write an explicit finite difference approximation to the following wave problem: Use second order approximation for boundary condition.Utt - Uxx = 0, for 0 < x < 1,u(x,0) = 0, Ut(x,0) = 0, u(0,t) = 0, u(1,t) = t.

SOLVED: Consider the Dirichlet wave problem on the finite interva…

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