EN 202 : Problem Set 3
نویسنده
چکیده
At this point, we require an explicit form of the characteristics. First, consider the solution to the ODE ȳξ(ξ, η) = 1. Integrating with respect to ξ, we find ȳ = ξ + φ(η). Applying the initial value on Γ, where y0(η) = 0 and ξ = 0, we find φ(η) = 0. Next, consider the solution to the ODE x̄ξ(ξ, η) = η . Integrating with respect to ξ, we find x̄ = ξη + ψ(η). Using the initial value on Γ, where x0(η) = η and ξ = 0, we find ψ(η) = η. Combining these results with Equation 1, we obtain the following solution to the PDE given by a parametric surface in the (x, y, u)-space, with tracing parameters (ξ, η).
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