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The second question Find u(x,y) satisfies PDE with given BCs-(Answered)

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Question

The second question



Find u(x,y) satisfies PDE with given BCs
delta-U(x,y)=0,
u(x,-2)=x
u(1,y)=0
u(x,2)=x+4
u(-1,y)=0

for x[-1,1]
y[-2,2]



???? ???? ???? ??? ?

 


 

??

 

? ?????????????????????

 


 

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1. You have to solve your homework problems on your own.

 

2. When working out solutions, you are encouraged (but not required) to use technical computing software (e.g., Mathematica, www.wolframalpha.com, or Maple) to conjecture the result, visualize your solution, or

 

validate your computations. If you formulate the question properly and interpret the output with care, these tools can often provide you with a complete answer. However, your solution will not be accepted if the

 

answer does not contain the detailed solution steps and proper mathematical reasoning.

 


 

? ??????????????????????

 

?????u(x? t)????????????????????????????????? ??????????????????????????????????????

 

?t?t u(x? t) + ?x?x?x?x u(x? t) = ??

 

??? x ? (?? ?) ??? t > ?

 


 

u(?? t) = u(?? t) = ??

 

?x?x u(?? t) = ?x?x u(?? t) = ??

 


 

u(x? ?) = x(x - ?)?

 

?t u(x? ?) = ??

 

???????????????????????????????????????????????????????????????????????????????????????????????????????????????????

 

????????????????? = ???? < ? ?????? > ???????????????????

 


 

? ??????????????????????

 

?????u(x? y)?????????????????????????????????????????????????????

 

??(x? y) = ??

 

??? x ? [-?? ?] ??? y ? [-?? ?]

 


 

u(x? -?) = x?

 

u(?? y) = ??

 

u(x? ?) = x + ??

 

u(-?? y) = ??

 


 

 

Paper#9209705 | Written in 27-Jul-2016

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