Converging shocks have long been a topic of interest in theoretical fluid mechanics, and are of prime importance in inertial confinement fusion. However, tracking converging shocks in numerical schemes poses several challenges. Numerical schemes based on shock capturing inherently diffuse out shocks to multiple grid cells, making it hard to track the shock. Converging shocks are significantly harder to track, as this numerical smearing is much more significant when converging shocks approach the axis of convergence. To mitigate this problem, we transform the conservation laws to a non-inertial frame of reference in which the accelerating shock is stationary. A system of equations is derived based on the transformed conservation laws coupled to the shock speed obtained from jump conditions and a characteristic-based derivation of a relation governing shock acceleration. We solve these equations using a finite volume method. Our numerical results compare favorably with the analytical value of Guderley exponent for self-similarly converging cylindrical hydrodynamic shocks. Results for fast magnetosonic shock in MHD are also presented and compared with results from geometrical shock dynamics (GSD). Results from our shock fitting method, developed without any approximation to the original ideal magnetohydrodynamics equations, provide further credibility to GSD applied to converging fast magnetosonic shocks. This sort of shock fitting is a precursor to future multidimensional stability analysis of imploding shocks.