The dormand prince method has a distinct advantage

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Unformatted text preview: y locating the discontinuity and restarting the solution there is also simpler with Runge-Kutta methods than with competing methods. Implicit Runge-Kutta methods are useful when high accuracy and A- or L-stability are needed simultaneously. This occurs with problems where fy (t y) has eigenvalues with large (neagative) real or imaginary parts. We will postpone a comparison of methods for these problems until examining multistep methods in Chapter 5. At this time, we'll note that software based on fth-, seventh- and ninth-order Radau methods 17] has done extremely well when solving sti IVPs. The STRIDE software 6] based on SIRK methods has been successful, but less so than the Radau methods. Problems 1. The aim of this problem is to write a subroutine or procedure for performing one step of a fourth-order variable step Runge-Kutta method applied to vector IVPs of the form y = f (t y) y(t0) = y0 : 0 1.1. Write a subroutine or procedure to perform one step of a fourth-order explicit Runge-Kutta metho...
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