Unformatted text preview: h = . 1 Solution Set x ( t ) = • x(t) y ( t ) ‚ and F ( t, x ) = • t 2 sin(x) + e t cos(y) 2 tx + e y ‚ The equation can then be written, in vector form, x ( t ) = F ( t, x ( t )) , x (0) = • 11 ‚ From (2) we can ﬁnd, with t = 0, x 1 = x + h * F ( t , x ) = • 11 ‚ + • t 2 sin(x ) + e t cos(y ) 2 t x + e y ‚ = • cos(1) e1 ‚ The following screen shot shows the results obtain by calling our Mathcad implementation of Euler’s method. Notice that in deﬁning the vectorvalued function F ( t, X ) , for Mathcad to know that X is an vector, in the deﬁnition, we use subscript to access the component of X , as shown in the screen shot....
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 Spring '11
 Dr.Han
 Differential Equations, Numerical Analysis, Derivative, Vectorvalued function, Numerical ordinary differential equations

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