hw9 - h = 0 . 5 to solve the ODE y = y + t for y (1) given...

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Homework #9 1. Use Euler’s method with stepsize h = 0 . 25 to solve the ODE y 0 = y + t for y (1) given y (0) = 1. 2. Consider the ODE y 0 = - 2 ty with y (0) = 2. The exact solution is y ( t ) = 2 e - t 2 . (a) Use Euler’s method with stepsize h = 0 . 5 to approximate y (1) and find the absolute error E (0 . 5) of this approximation. (b) Use Euler’s method with stepsize h = 0 . 25 to approximate y (1) and find the absolute error E (0 . 25) of this approximation. (c) Compute E (0 . 5) /E (0 . 25). 3. Use Midpoint Method with stepsize h = 0 . 5 to solve the ODE y 0 = y + t for y (1) given y (0) = 1. 4. Use Trapezoid Method with stepsize
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Unformatted text preview: h = 0 . 5 to solve the ODE y = y + t for y (1) given y (0) = 1. 5. (Math 274) Consider y = f ( x,y ) at x = x 2 , where x < x 1 < x 2 with regular spacing h . Integrate both sides from x to x 2 . Use Simpson’s Rule to approximate the right hand side integral. Finally, write down the corresponding implicit approximation scheme for solving this ODE at x 2 in terms of data at x ,x 1 ,x 2 . 1...
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This note was uploaded on 10/17/2010 for the course MATH 174 taught by Professor Staff during the Spring '08 term at UCSD.

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