Solving PDEs Involving Characteristics, Expansion Waves and Shocks

pivoxa15
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Do people find solving PDEs involving characteristics, expansion waves and shocks difficult? I find it extremely difficult. It is hard to get one's head around it. Are there any ways of making it easier?
 
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To the shock problems, according to my experience, discrete singular convolution (DSC) method would be a feasible and even better choice for such kind of problems!
 

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