3. (a) Determine all value(s) of x for which the following PDE is hyperbolic: [4 points) U... - 2xUxy - (3r- 2)Uyy = 0.

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3 A Determine All Value S Of X For Which The Following Pde Is Hyperbolic 4 Points U 2xuxy 3r 2 Uyy 0 1 (36.63 KiB) Viewed 26 times

3. (a) Determine all value(s) of x for which the following PDE is hyperbolic: [4 points) U... - 2xUxy - (3r- 2)Uyy = 0. (1) (b) Consider the PDE U21 - 2xUry – 3.r?Uyy = 0, -" <x<0,42 0 (2) U(x,0) = r, - <x< U,(3,0) = 0, -« <r<%. i. Suppose the characteristic curves that pass through the points A(-1,0) and B(-2,0) intersect at a point P(XP, yp). Find the exact value of xp and yp. [8 points) ii. Letting h = Ar and k = Ay and using the central differences, write down a consistent scheme for the PDE (2). You need not prove consistency. [5 points) iii. Construct a consistent finite difference approximation for U, that uses the values tij, Ui j+1, and Hij+2. You need not prove consistency. From the principal error term, determine the order of accuracy of this approximation. 18 points)