ts = seq( -1, 1, length.out=100 )

phi_1 = 2 * ts
phi_2 = 2 * ( ts^2 + ts )
phi_3 = ( 4 * ts^3 / 3 + 2 * ts^2 + 2 * ts )
phi_4 = ( 2 * ts^4 / 3 + 4 * ts^3 / 3 + 2 * ts^2 + 2 * ts )
phi_inf = exp(2*ts) - 1 

all_phis = c( phi_1, phi_2, phi_3, phi_4, phi_inf )
all_phi_errors = c( phi_1 - phi_inf, phi_2 - phi_inf, phi_3 - phi_inf, phi_4 - phi_inf )
all_phi_abs_errors = abs(all_phi_errors)

#postscript("../../WriteUp/Graphics/Chapter2/chap_2_sect_8_prob_3_plot.eps", onefile=FALSE, horizontal=FALSE)

par(mfrow=c(1,2))

# The functions:
#
min_y = min( all_phis )
max_y = max( all_phis )

plot( ts, phi_1, type='l', ylim=c( min_y, max_y ), col='red', xlab='t', ylab='phi_n(t)' )
lines( ts, phi_2, type='l', col='blue' )
lines( ts, phi_3, type='l', col='green' )
lines( ts, phi_4, type='l', col='darkblue' )
lines( ts, phi_inf, type='l', col='black' )
legend( 'topleft', c('phi_1(t)', 'phi_2(t)', 'phi_3(t)', 'phi_4(t)', 'phi(t)'),
lwd=2, lty=1, col=c('red', 'blue', 'green', 'darkblue', 'black'))
grid()

# The errors:
#
min_y = min( all_phi_abs_errors )
max_y = max( all_phi_abs_errors )

plot( ts, abs(phi_inf - phi_1), type='l', ylim=c( min_y, max_y ), col='red', xlab='t', ylab='|phi(t) - phi_n(t)|' )
lines( ts, abs(phi_inf - phi_2), type='l', col='blue' )
lines( ts, abs(phi_inf - phi_3), type='l', col='green' )
lines( ts, abs(phi_inf - phi_4), type='l', col='darkblue' )
legend( 'topleft', c('phi_1 aerr', 'phi_2 aerr', 'phi_3 aerr', 'phi_4 aerr'), lwd=2, lty=1, col=c('red', 'blue', 'green', 'darkblue'))
grid()

par(mfrow=c(1,1))

#dev.off()