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MusclHancock

-              v19
+              v20
 [[latex($ \frac{\partial \vec{u}}{\partial t} + \frac{\partial f(\vec{u})}{\partial x} = 0 $)]]
 where u is the vector of conserved variables and f is the flux function. We solve this method adhering to the IVBP, the Riemann Problem, using the fully discrete, explicit, conservative formula:
+where u is the vector of conserved variables and f is the flux function. Adhering to the IVBP known as the Riemann Problem, we solve this system of equations using the fully discrete, explicit, conservative formula:
 [[latex($ u_i^ {n+1} = u_i ^n + \frac{\triangle t}{\triangle x}[f_{i-1/2} - f_{i+1/2}]$)]]
 To produce 2nd-order accuracy, an outline of the MH scheme is as follows.
+for each element of u. When f is the numerical flux. For the 1st order Godunov scheme studied previously, f was taken to simply be the physical flux of 2 adjacent cells, evaluated using the solution to the Local Riemann Problem at the intercell boundary. We have seen various approximation methods to this Godonov scheme, some which estimate the solutipn of the Riemann problem itself along these intercell boundaries, and others that approximate the numerical flux at these boundaries. Next, we will see how the MH scheme produces a 2nd-order accurate solution to the problem. The MH scheme proceeds as follows, being broken down into 3 distinct steps.
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