Practice Problems - Wave Equation
MTH3102 Spring 2009
(1) Determine the solution of the following initial value problems:
(a) utt −c2uxx = 0, u(x, 0) = sin x ut(x, 0) = x2.
(b) utt −c2uxx = 0, u(x, 0) = cos x ut(x, 0) = x.
(2) Determine the solution of the initial- boundary value problem:
utt −16uxx = 0,0< x < ∞, t > 0
u(x, 0) = sin x, 0< x < ∞
ut(x, 0) = x2,0< x < ∞
u(0, t)=0, t > 0
(3) Determine the solution of the initial- boundary value problem:
utt −9uxx = 0,0< x < ∞, t > 0
u(x, 0) = 0,0< x < ∞
ut(x, 0) = x3,0< x < ∞
ux(0, t)=0, t > 0
(4) Solve the following initial boundary value problem by method of
seperation of variables:
utt −c2uxx = 0,0< x < π, t > 0
u(x, 0) = 3 sin x, 0< x < π
ut(x, 0) = 0,0< x < π
u(0, t) = u(π, t) = 0.
(5) Solve the following initial boundary value problem by method of
seperation of variables:
utt −c2uxx = 0,0< x < π, t > 0
u(x, 0) = 0,0< x < π
ut(x, 0) = 8 sin2x, 0< x < π
u(0, t) = u(π, t) = 0.
(6) Solve the following initial boundary value problem by method of
seperation of variables:
utt −c2uxx = 0,0< x < π, t > 0
u(x, 0) = sin x, 0< x < π
ut(x, 0) = x2−πx, 0< x < π
u(0, t) = u(π, t) = 0.
(7) Solve the following initial boundary value problem by method of
seperation of variables:
utt −c2uxx = 0,0< x < π, t > 0
u(x, 0) = cos x, 0< x < π
ut(x, 0) = 0,0< x < π
ux(0, t) = ux(π, t) = 0.
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