T - IfB

References for R-K method• G.E. Forsythe, M.A. Malcolm and C.B. Moler, „ComputerMethods for Mathematical Computations“ (Prentice Hall,Englewood Cliffs, NJ, 1977), Chapter 6• E. Hairer, S.P. Nørsett and G. Wanner, “Solving OrdinaryDifferential Equations I” (Springer, Berlin, 1993)• W.H. Press, B.P.Flannery, S.A Teukolsky and W.T. Vetterling,“Numerical Recipes” (Cambridge University Press, Cambridge,1988), Sect. 16.1 and 16.2• J.C. Butcher, „The Numerical Analysis of Ordinary DifferentialEquations“ (Wiley, New York, 1987)• J.D. Lambert, „Numerical Methods for Ordinary DifferentialEquations“ (John Wiley & Sons, New York, 1991)• L.F. Shampine, „Numerical Solution of Ordinary DifferentialEquations“ (Chapman and Hall, London, 1994)952nd order Runge - Kutta methodExtrapolate using Euler methodto the value halfway, i.e. . at t + Δt / 2:1 1y ( t t) y ( t) tf( y ( t), t)i i i2 2Evaluate derivative in Euler method at this value:1 12 2y t t y t t f y t t t t O t3i( ) i( ) (i( ), ) ( )96