! ! Numerical Mathematics and Computing, Fifth Edition ! Ward Cheney & David Kincaid ! Brooks/Cole Publ. Co. ! Copyright (c) 2003. All rights reserved. ! For educational use with the Cheney-Kincaid textbook. ! Absolutely no warranty implied or expressed. ! ! Section 10.1 ! ! File: taylor.f90 ! ! Taylor series method (order 4) for solving an ordinary differential equation program main real :: a=1.0,b=2.0, x=-4.0, h, t, x1,x2,x3,x4 integer :: n=100, k h=(b-a)/real(n) t=a print*,"0",t,x do k=1,n x1 = 1.0 + x*x + t**3 x2 = 2.0*x*x1 + 3.0*t*t x3 = 2.0*x*x2 + 2.0*x1*x1 + 6.0*t x4 = 2.0*x*x3 + 6.0*x1*x2 + 6.0 x = x + h*(x1 + (h/2.0)*(x2 + (h/3.0)*(x3 + (h/4.0)*x4))) t = a + real(k)*h print *, k,t,x end do end program main