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Differential Equations
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OpenStudy (anonymous):
Consider the initial value problem dy/dt=a*t^(a-1), y(0)=0, where a>0. The true solution is y(t)=t^a. Use the Euler method to solve the initial value problem for a=2.5,1.5,1.1 with stepsize h=0.2,0.1,0.05. Compute the solution errors at the nodes, and determine numerically the convergence orders of the Euler method for these problems. Does anyone have any ideas?
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OpenStudy (unklerhaukus):
Forward Euler method for \(y'=f(t,y)\)\[\hat y_{j+1}=\hat y_j+h\cdot f(t_j,\hat y_j)\] Your equation is \[y'=a\times t^{a-1}\]
OpenStudy (unklerhaukus):
\[\hat y_0=y(0)\]
OpenStudy (unklerhaukus):
\[\hat y_1=\hat y_0+h(a(0)^{a-1})\] \[\hat y_2=\hat y_1+h(a(1)^{a-1})\] ...
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