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# This is easier to do with runge kutta methods than

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Unformatted text preview: d. You may use the classical, Fehlberg, Dormand and Prince, or other formula as long as it is fourth order. 55 1.2. Test your procedure using xed step integration with step sizes h = 1/2, 1/4, 1/8, : : : using the test IVPs y =y 0 and y(0) = 1 0 1 d2y + 2k dy + n2 y = 0 0<t<3 dt2 dt y(0) = 1 dyoverdt(0) = 0: For the second example use n = 10, k = 6 and n = 10, k = 8. In each case, present results (tables and/or graphs) of the global error and number of function evaluations as functions of h. Estimate the rate of convergence of the method and compare it with the theoretical rate. 1.3. Replace the xed step size strategy above with a variable step size technique of your choice. Base step size selection on control of the local error, which may be estimated using either step doubling or embedding. Compare the performance of your code on the above problems with the xed step performance. 56 Bibliography 1] M. Abromowitz and I. Stegun. Handbook of Mathematical Functions. Dover, New York, 1995. 2] R. Alexander. Diagonally implicit runge-kutta meth...
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