166_pdfsam_math 54 differential equation solutions odd

166_pdfsam_math 54 differential equation solutions odd -...

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Chapter 3 Table 3–J : 4th order Runge-Kutta approximations to the solution of y 0 =cos(5 y ) x , y (0) = 0, on [0 , 3] with h =0 . 1. x n x n y n y n x n x n y n y y n 0 0 1.5 0 . 02668 0.1 0.09134 1.6 0 . 85748 0.2 0.15663 1.7 0 . 17029 0.3 0.19458 1.8 0 . 30618 0.4 0.21165 1.9 0 . 53517 0.5 0.21462 2.0 0 . 81879 0.6 0.20844 2.1 1 . 02887 0.7 0.19629 2.2 1 . 17307 0.8 0.18006 2.3 1 . 30020 0.9 0.16079 2.4 1 . 45351 1.0 0.13890 2.5 1 . 69491 1.1 0.11439 2.6 2 . 03696 1.2 0.08686 2.7 2 . 30917 1.3 0.05544 2.8 2 . 50088 1.4 0.01855 2.9 2 . 69767 3.0 2 . 99510 17. Taylor method of order 2 has recursive formulas given by equations (5) and (6) on page 135 of the text: that is x j +1 = x j + h and y j +1 = y j + hf ( x j ,y j )+ h 2 2! f 2 ( x j ,y j ) . With f ( x, y )= y ,wehave
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