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Differential Equations Lecture Work Solutions 287

Differential Equations Lecture Work Solutions 287 - 9 8 7 6...

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-1 0 1 2 3 4 5 6 7 8 9 -1 0 1 2 3 4 5 6 7 8 9 x t x-ct<0 x-ct>0 Figure 57: Domain of influence for problem 3 3b. u ( x, t ) = f ( x + ct ) + f ( x ct ) 2 x > ct f ( x + ct ) + f ( ct x ) 2 x < ct where u ( x, t ) = 1 Region I 1 2 Region II 0 otherwise In order to find the regions I and II mentioned above, we use the idea of domain of influence. Sketch both characteristics from the end points of the interval (2,3) and remember
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