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Consider the linear system of equations311 T2 T3 211 + ATz + T3 T1 212 513(a) Write down the components of the Gauss-= Seidel iteration equation: Do not do any iter...

Question

Consider the linear system of equations311 T2 T3 211 + ATz + T3 T1 212 513(a) Write down the components of the Gauss-= Seidel iteration equation: Do not do any iterations, just write down the iteration mechanism_ (b) Starting with an initial vector 2(0) [0, 0 , 0]2' apply the Gauss-Seidel iteration until the approximate relative error falls below 4%

Consider the linear system of equations 311 T2 T3 211 + ATz + T3 T1 212 513 (a) Write down the components of the Gauss-= Seidel iteration equation: Do not do any iterations, just write down the iteration mechanism_ (b) Starting with an initial vector 2(0) [0, 0 , 0]2' apply the Gauss-Seidel iteration until the approximate relative error falls below 4%



Answers

Let $y(t)$ be the solution to $\frac{d y}{d t}=t e^{-y}$ satisfying $y(0)=0$. (a) Use Euler's Method with time step $h=0.1$ to approximate $y(0.1), y(0.2), \ldots, y(0.5)$ (b) Use Separation of Variables to find $y(t)$ exactly. (c) Compute the errors in the approximations to $y(0.1)$ and $y(0.5)$.

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