N38 - ME 510 NUMERICAL METHODS FOR ME II HIGHER -ORDER ODEs...

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ME – 510 NUMERICAL METHODS FOR ME II gG±²³´µG³´¶·G¸¹´ºG»¼½ Fall 2007 HIGHER -ORDER ODE’s g G 2 2 d y(x) = f x, y(x), y'(x) d x Second-order ODE: Two conditions must be specified for the solution: At x = 0 y(0) = y 0 and 0 d y = y'(0) d x x ± } Initial-value problem At x = 0 y(0) = y 0 and } Boundary-value problem At x = L y(L) = y L Note that derivative conditions may also be specified at the boundaries ME – 510 NUMERICAL METHODS FOR ME II gG±²³´µG³´¶·G¸¹´ºG»¼½ Fall 2007 SECOND-ORDER ODE - INITIAL VALUE PROBLEM g G 2 2 d y(x) = f x, y(x), y'(x) d x At x = 0 y(0) = y 0 and 0 d y = y'(0) d x x ± Define 0 dy(x) = z(x) = g(x, y, z) , z(0) = z d x g G 0 d z(x) = f x, y(x), z(x) , y(0) = y d x All the methods discussed so far are applicable.
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ME – 510 NUMERICAL METHODS FOR ME II gG±²³´µG³´¶·G¸¹´ºG»¼½ Fall 2007 SECOND-ORDER ODE - INITIAL VALUE PROBLEM
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N38 - ME 510 NUMERICAL METHODS FOR ME II HIGHER -ORDER ODEs...

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