  The radio evolution of, so far the youngest known, Galactic supernova remnant
(SNR) G1.9+0.3 is investigated by using three-dimensional (3D) hydrodynamic
modelling and non-linear kinetic theory of cosmic ray (CR) acceleration in
SNRs. We include consistent numerical treatment of magnetic field amplification
(MFA) due to resonant streaming instability. Under the assumption that SNR
G1.9+0.3 is the result of a Type Ia supernova explosion located near the
Galactic Centre, using widely accepted values for explosion energy 10$^{51}$
erg and ejecta mass 1.4 $M_{\odot}$, the non-thermal continuum radio emission
is calculated. The main purpose of this paper is to explain radio flux
brightening measured over recent decades and also predict its future temporal
evolution. We estimate that the SNR is now $\sim$ 120 yr old, expanding in an
ambient density of 0.02 cm$^{-3}$, and explain its steep radio spectral index
only by means of efficient non-linear diffusive shock acceleration (NLDSA). We
also make comparison between simulations and observations of this young SNR, in
order to test the models and assumptions suggested. Our model prediction of a
radio flux density increase of $\sim$ 1.8 per cent yr$^{-1}$ during the past
two decades agrees well with the measured values. We synthesize the synchrotron
spectrum from radio to X-ray and it fits well the VLA, MOST, Effelsberg,
Chandra and NuSTAR measurements. We also propose a simplified evolutionary
model of the SNR in gamma rays and suggest it may be a promising target for
gamma-ray observations at TeV energies with the future generation of
instruments like Cherenkov Telescope Array. SNR G1.9+0.3 is the only known
Galactic SNR with the increasing flux density and we present here the
prediction that the flux density will start to decrease approximately 500 yr
from now. We conclude that this is a general property of SNRs in free expansion
phase.
