# 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('improved_euler.R') t0 = 0.0 y0 = 1.0 t1 = 2.0 # Where do we want to evaluate the solution: # x_grid = c( seq( t0, 0.5, by=0.1 ), 1.0, 1.5, 2.0 ) # TODO: fix limits # The improved Euler method: # dy.dt = function(t, y){ 1-t+4*y } h=0.025 res = improved_euler(dy.dt, h=h, start=t0, y0=y0, end=t1) ie_yhat_h1 = knn.reg( as.matrix( res\$xs ), y=res\$ys, test=as.matrix( x_grid ), k=1, algorithm='brute' ) h=0.01 res = improved_euler(dy.dt, h=h, start=t0, y0=y0, end=t1) ie_yhat_h2 = knn.reg( as.matrix( res\$xs ), y=res\$ys, test=as.matrix( x_grid ), k=1, algorithm='brute' ) A = rbind( ie_yhat_h1\$pred, ie_yhat_h2\$pred ) rownames(A) = NULL R = cbind( c( 0.025, 0.01 ), A ) # TODO: should be 0.1 colnames(R) = c( 'h', sprintf( 'y(%.2f)', x_grid ) ) print('Problem 13 (Improved Euler):') print(R)