Consider the IVP on [0, 1]: y = -y1 - Y2 y2 = Y1 - Y2...

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Consider the IVP on [0, 1]: y₁ = -y1 - Y2 y2 = Y1 - Y2 31(0) = 1,2(0)= = 0 (a) Verify that the solution is y1(t) = et cost, y2(t) = et sint. (b) Apply Euler's Method with step sizes h = 0.1 and 0.01 to the initial value problem. Plot the approxi- mate solutions and the correct solution on [0, 1]. You can use the MATLAB code euler2.m to calculate the two approximations. (c) Find the global truncation error at t = 1. (d) Is the reduction in error for h = 0.01 consistent with the order of Euler's Method? Consider the IVP on [0, 1]: y₁ = -y1 - Y2 y2 = Y1 - Y2 31(0) = 1,2(0)= = 0 (a) Verify that the solution is y1(t) = et cost, y2(t) = et sint. (b) Apply Euler's Method with step sizes h = 0.1 and 0.01 to the initial value problem. Plot the approxi- mate solutions and the correct solution on [0, 1]. You can use the MATLAB code euler2.m to calculate the two approximations. (c) Find the global truncation error at t = 1. (d) Is the reduction in error for h = 0.01 consistent with the order of Euler's Method?

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a To verify that the solution is y t e cost and y t e sint we can directly substitute these function... View the full answer