  In this work, a simple fourth-order accurate finite volume semi-discrete
scheme is introduced to solve astrophysical magnetohydrodynamics (MHD) problems
on Cartesian meshes. Hydrodynamic quantities like density, momentum and energy
are discretised as volume averages. The magnetic field and electric field
components are discretised as area and line averages respectively, so as to
employ the constrained transport technique, which preserves the solenoidality
of the magnetic field to machine precision. The present method makes use of a
dimension-by-dimension approach employing a 1-D fourth-order accurate centrally
weighted essentially non-oscillatory (1D-CWENO4) reconstruction polynomial. A
fourth-order accurate, strong stability preserving (SSP) Runge-Kutta method is
used to evolve the semi-discrete MHD equations in time. Higher-order accuracy
of the scheme is confirmed in various linear and nonlinear multi-dimensional
tests and the robustness of the method in avoiding unphysical numerical
artifacts in the solution is demonstrated through several complex MHD problems.
