In this study, the radial basis function (RBF) approximation is applied for solving the unsteady fluid flow and magnetohydrodynamic (MHD) convection flow problems with the use of explicit Euler time discretization and relaxation parameters to accelerate the convergence. The stability analysis is also carried out in terms of the spectral radius of related RBF discretized coefficient matrices. The optimal choices of the time increment, relaxation parameters and physical problem parameters are found for achieving stable solutions. It is observed that the maximum eigenvalues of the coefficient matrices decrease with an increase in the time increment when the relaxation parameters are decreasing. Although the time derivative is discretized using explicit Euler method, one does not need to use small time increment for obtaining stable results. The flow, isotherms and pressure behaviors are simulated at steady-state for several values of problem parameters using time increment and relaxation parameters which lead to stable solutions.