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This paper deals with the numerical computations of two space dimensionaltime dependent parabolic partial differential equations by adopting adopting anoptimal five stage fourth-order strong stability preserving Runge Kutta(SSP-RK54) scheme for time discretization, and three methods of differentialquadrature with different sets of modified B-splines as base functions, forspace discretization: namely i) mECDQM: (DQM with modified extended cubicB-splines); ii) mExp-DQM: DQM with modified exponential cubic B-splines, andiii) MTB-DQM: DQM with modified trigonometric cubic B-splines. Specially, weimplement these methods on convection-diffusion equation to convert them into asystem of first order ordinary differential equations,in time which can besolved using any time integration method, while we prefer SSP-RK54 scheme. Allthe three methods are found stable for two space convection-diffusion equationby employing matrix stability analysis method. The accuracy and validity of themethods are confirmed by three test problems of two dimensionalconvection-diffusion equation, which shows that the proposed approximatesolutions by any of the method are in good agreement with the exact solutions.

Algorithms based on DQM with new sets of base functions for solving parabolic partial differential equations in $(2+1)$ dimension