3 (10) - V(tk -2(u(Aj2 + u(Bj2 + u(C1 )2)-u(A1 )u(B1)-u(A1 )u(C1)-u(B1 )u(C))

Go to case 2

Case 2: considering that vk > u(B1) > u(A1) and vk < u(C1), the upwind scheme (8) is equivalent to:

Computing the discriminant of equation (11) there are two possibilities:

vk = -(u(A1) + u(B1)) + -V2t2 -(u(B1)-u(A1 ))2 (12)

Note that case 2 is similar to the update procedure of the 2D Fast Marching (Sethian, 1999).

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