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Economics Dynamics Problems 201

Economics Dynamics Problems 201 - Systems of rst-order...

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Systems of first-order differential equations 185 Hence, x 1 = x 0 + f ( x 0 , y 0 ) t = 2 + 3(0 . 01) = 2 . 03 y 1 = y 0 + g ( x 0 , y 0 ) t = 2 + 3(0 . 01) = 2 . 03 and f ( x 1 , y 1 ) = − 2(2 . 03) 2 . 03 + 9 = 2 . 91 g ( x 1 , y 1 ) = − 2 . 03 + 2 . 03 + 3 = 3 giving x 2 = x 1 + f ( x 1 , y 1 ) t = 2 . 03 + 2 . 91(0 . 01) = 2 . 0591 y 2 = y 1 + g ( x 1 , y 1 ) t = 2 . 03 + 3(0 . 01) = 2 . 06 This process is repeated. But all this can readily be set out on a spreadsheet, as shown in figure 4.33. The first two columns are simply the differential equations. Columns (3) and (4) employ the Euler approximation using relative addresses and the absolute address for t . The x - y plot gives the trajectory of the system in the phase plane, with initial value (
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