  This paper deals with the numerical computations of two space dimensional
time dependent parabolic partial differential equations by adopting adopting an
optimal five stage fourth-order strong stability preserving Runge Kutta
(SSP-RK54) scheme for time discretization, and three methods of differential
quadrature with different sets of modified B-splines as base functions, for
space discretization: namely i) mECDQM: (DQM with modified extended cubic
B-splines); ii) mExp-DQM: DQM with modified exponential cubic B-splines, and
iii) MTB-DQM: DQM with modified trigonometric cubic B-splines. Specially, we
implement these methods on convection-diffusion equation to convert them into a
system of first order ordinary differential equations,in time which can be
solved using any time integration method, while we prefer SSP-RK54 scheme. All
the three methods are found stable for two space convection-diffusion equation
by employing matrix stability analysis method. The accuracy and validity of the
methods are confirmed by three test problems of two dimensional
convection-diffusion equation, which shows that the proposed approximate
solutions by any of the method are in good agreement with the exact solutions.

Numerical Analysis