# I use the function knn.reg to evaluate the numerical solution at a fixed grid of points # if( !require('FNN') ){ install.packages('FNN', dependencies=TRUE, repos='http://cran.rstudio.com/') } library(FNN) source('../Chapter2/euler.R') t0 = 0 y0 = 1 t1 = 1.0 dy.dt = function(t, y){ cos(5*pi*t) } h=0.2 res = euler(dy.dt, h=h, start=t0, y0=y0, end=t1) t_grid_1 = seq( t0, 0.6, by=h ) e_yhat_h1 = knn.reg( as.matrix( res\$xs ), y=res\$ys, test=as.matrix( t_grid_1 ), k=1, algorithm='brute' ) print('Part (b):') print(e_yhat_h1\$pred[-1]) h=0.1 res = euler(dy.dt, h=h, start=t0, y0=y0, end=t1) t_grid_2 = seq( t0, 0.4, by=h ) e_yhat_h2 = knn.reg( as.matrix( res\$xs ), y=res\$ys, test=as.matrix( t_grid_2 ), k=1, algorithm='brute' ) print('Part (c):') print(e_yhat_h2\$pred[-1]) # Truth: # t_truth = seq( 0, 1, length.out=100 ) y_truth = sin(5*pi*t_truth)/(5*pi) + 1 y_truth_ds = knn.reg( as.matrix( t_truth ), y=y_truth, test=as.matrix(t_grid_2), k=1, algorithm='brute' ) #postscript("../../WriteUp/Graphics/Chapter8/chap_8_sect_1_prob_22_plot.eps", onefile=FALSE, horizontal=FALSE) ymin = min( c(y_truth, e_yhat_h1\$pred, e_yhat_h2\$pred) ) ymax = max( c(y_truth, e_yhat_h1\$pred, e_yhat_h2\$pred) ) plot(t_truth, y_truth, type='l', xlab='t', ylab='y(t)', ylim=c(ymin, ymax), col='green') lines(t_grid_1, e_yhat_h1\$pred, type='b', col='blue', pch=19) lines(t_grid_2, e_yhat_h2\$pred, type='b', col='red', pch=19) legend( 'topright', c('Truth', 'Euler (h=0.2)', 'Euler (h=0.1)'), lty=c(1, 1, 1), col=c('green', 'blue', 'red') ) grid() #dev.off()