Comments
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My matrix is [0,4,2,2,4] [3,0,1,4,4] [1,2,0,1,2] [2,2,4,0,1] [4,2,4,3,0] The ranking for the league is: Team 1: rating = 0.5184926437130086 Team 2: rating = 0.5124889651579149 Team 5: rating = 0.5112730954121437 Team 4: rating = 0.3571588647222856 Team 3: rating = 0.28205993381697697 So team 1 is the best. Go team 1!!
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Given my conditions, the temperature in the lower right hand corner is 0.90549
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Given my parameters, at t=1s the temperature will be 0.00053
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Given my domain and parameters, the temperature at t=1s is about 0.00
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A metal bar of length 1 lies along the unit interval. Its temperature distribution is $$g(x)=5x^2-4x$$ At t=0, its left end and right end set to temp 0. Sketch the distribution at times $$t=0, t=0.01, t=0.1, and t=10.$$
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My heat flow equation is $$ u_t=4u_{xx}+4$$ And my boundary conditions are $$u(0,t)=-2$$ and $$u(1,t)=5$$ when $u_t=0$, solving for $u_{xx}$ gives us $u_{xx}=-1$. Integrating twice, we get $$u(x) = -x^2+ax+b$$ By using our initial conditions we get $$u(x)=-x^2+(17/2)x-(7/2)$$ which is our steady state temperature…
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The displacement is t=1.7s and the midpoint is approximately -0.271.