chapter iv. runge example, with cubic hermite interpolation c from * a practical guide to splines * by c. de boor integer i,istep,j,n,nm1 real aloger,algerp,c(4,20),decay,divdf1,divdf3,dtau,dx,errmax,g,h * ,pnatx,step,tau(20) data step, istep /20., 20/ g(x) = 1./(1.+(5.*x)**2) print 600 600 format(28h n max.error decay exp.//) decay = 0. do 40 n=2,20,2 c choose interpolation points tau(1), ..., tau(n) , equally c spaced in (-1,1), and set c(1,i) = g(tau(i)), c(2,i) = c gprime(tau(i)) = -50.*tau(i)*g(tau(i))**2, i=1,...,n. nm1 = n-1 h = 2./float(nm1) do 10 i=1,n tau(i) = float(i-1)*h - 1. c(1,i) = g(tau(i)) 10 c(2,i) = -50.*tau(i)*c(1,i)**2 c calculate the coefficients of the polynomial pieces c do 20 i=1,nm1 dtau = tau(i+1) - tau(i) divdf1 = (c(1,i+1) - c(1,i))/dtau divdf3 = c(2,i) + c(2,i+1) - 2.*divdf1 c(3,i) = (divdf1 - c(2,i) - divdf3)/dtau 20 c(4,i) = (divdf3/dtau)/dtau c c estimate max.interpolation error on (-1,1). errmax = 0. do 30 i=2,n dx = (tau(i)-tau(i-1))/step do 30 j=1,istep h = float(j)*dx c evaluate (i-1)st cubic piece c pnatx = c(1,i-1)+h*(c(2,i-1)+h*(c(3,i-1)+h*c(4,i-1))) c 30 errmax = amax1(errmax,abs(g(tau(i-1)+h)-pnatx)) aloger = alog(errmax) if (n .gt. 2) decay = * (aloger - algerp)/alog(float(n)/float(n-2)) algerp = aloger 40 print 640,n,errmax,decay 640 format(i3,e12.4,f11.2) stop end