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MusclHancock

v28	v29
36	36	[[latex($u_i(x) = u_i^n + (x - x_i) \frac{\triangle _i }{\triangle x}, x \in [0, \triangle x]$)]]
37	37
38		where [[latex($ \triangle _i $)]] is called a 'slope' for [[latex($ u_i ^n $)]], that is, for the elements of [[latex($ \vec{u} $)]] in cell i on the nth time level. Using a linear function produces 2 extreme values of each cell, one on the left and on the right: [[latex($ u_l $)]] and [[latex($ u_r $)]], respectively. These values are crucial in the MH scheme and their role will be presented shortly. A schematic of the situation is as follows:
	38	where [[latex($ \triangle _i $)]] is called a 'slope' for [[latex($ u_i ^n $)]], that is, for the elements of [[latex($ \vec{u} $)]] in cell i on the nth time level. Using a linear function produces 2 extreme values of each cell, one on the left and on the right: [[latex($ u_l $)]] and [[latex($ u_r $)]], respectively. These values are crucial in the MH scheme and their role will be presented shortly. Their values are given by [[latex($ u_l = u_i(0) = u_i ^n - \{1}{2} \triangle_ i $)]] and [[latex($ u_r = u_i(0) = u_i ^n + \{1}{2} \triangle_ i $)]]. A schematic of the situation is as follows:
39	39
40	40	[[Image(MusclReconstruction.png, 35%)]]