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assign9-09

# assign9-09 - MATH 573 ASSIGNMENT 9 w f(x w z Heuns method...

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MATH 573 ASSIGNMENT 9 1. Let Y = w z and F ( x, Y ) = f 1 ( x, w, z ) f 2 ( x, w, z ) . Heun’s method for the system of differential equations Y = F ( x, Y ), with initial condition Y ( x 0 ) = Y 0 , is given by: Y n +1 = Y n + h 2 F ( x n , Y n ) + h 2 F ( x n + h, Y n + hF ( x n , Y n )) . Find approximations to w ( h ) and z ( h ) for the system w = z, z = - cw, w (0) = a, z (0) = b, where a, b, c are given constants. 2. Consider the approximation of the initial value problem y = f ( x, y ), y ( x 0 ) = y 0 , by a class of explicit linear multistep methods of the form: y n +1 = a 0 y n + a 1 y n - 1 + h [ b 0 f n + b 1 f n - 1 ] . If the constant a 0 is considered fixed, determine values of the constants
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