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!
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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