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Problems related to partial differential equations (pdes) from a university course. The problems involve identifying the order of certain equations, computing and plotting characteristics for given pdes, and writing a computer program to solve a specific pde. The problems cover various techniques and methods for solving pdes.
Typology: Assignments
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Problems due Sept 12, 2007
Problem:1.0-
Identify the order of the following equation(s):
∂ψ ∂t
u ∂ψ ∂x
v ∂ψ ∂y
= ψo − ψ (1.1)
∂v ∂t
g∇η = 0 (1.2) ∂η ∂t
∇ · (v(h + η)) = 0 (1.3) (1.4)
∂u ∂t
− f v + g
∂η ∂x
∂v ∂t
∂η ∂y
∂η ∂t
Problem:1.0-
Compute and plot the characteristics for
i) ∂T ∂t
∂x
where U (x) = 1 + sin(x)/ 2 (Plot for 0 < x < 2 π)
ii)
∂h ∂t
∂u ∂x
∂u ∂t
∂h ∂x
where H(x) = 10 − x for 0 < x < 5 iii)
∂u ∂t
