Abstract This paper deals with the solution of time-dependent problems. The multiquadric radial basis function method is formulated, with a new approach for transient problems. One- and two-dimensional problems are considered. The forward difference and the Crank–Nicolson time-marching schemes for parabolic cases are considered. The central difference integration method of the Newmark family is considered for hyperbolic problems. The method proves its accuracy in four numerical examples.