14.To find the approximate values, set y15y2e2x11 and use EULERT and IMPEULT with initial valuesx50 and y521 and step size 0.1 for 20 points. The exact values are given byy5ex2e2x21.15. (a)}ddyx} 52y2(x21)}dyy2} 52(x21)dxEy22dy5E(2x22) dx2y215x222x1CInitial value:y(2)52}12}252222(2)1C25CSolution:2y215x222x12 ory}x2221x12}y(3)}32221(3)12}52}15}520.2(b)To find the approximation, set y152y2(x21) and use EULERT with initial values x52 and y12}and step size 0.2 for5 points. This gives y(3) <20.1851; error <0.0149.(c)Use step size 0.1 for 10 points. This gives y(3) <20.1929; error <0.0071.(d)Use step size 0.05 for 20 points. This gives y(3) <20.1965; error <0.0035.Section 6.6277xy (Euler)y12improvedEulery(exact)02121210.121.100021.116121.11620.221.232121.270021.27040.321.404521.471521.47230.421.627221.732521.73370.521.912522.067822.06960.622.275622.495422.49800.722.735123.037823.04140.823.314223.722423.72750.924.040924.583224.59001.0
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.