[01] S. Kanzari, National Research Institute for Rural Engineering, Water and Forestry, INRGREF, University of Carthage, Ariana, Tunisia. [02] S. Ben Mariem, National Research Institute for Rural Engineering, Water and Forestry, INRGREF, University of Carthage, Ariana, Tunisia. [03] H. Sahraoui, National Research Institute for Rural Engineering, Water and Forestry, INRGREF, University of Carthage, Ariana, Tunisia.

In this study, we apply Reduced Differential Transform Method (RDTM) for solving partial differential equations in different dimensions with variable coefficients. RDTM is employed to obtain the exact solution of simple homogeneous advection and heat-like equations. The RDTM produces a solution with few and easy computation. The method is simple, accurate and efficient.

Reduced Differential Transform Method, Advection Equation, Heat-Like Equations, Analytic Solutions

[01] Alomari A.K., Noorani M.SM. and Nazar R., 2008. Solution of heat-like and wave-like equations with variable coefficients by means of the homotopy analysis method. Chinese physics letters, (25): 589-593. [02] Benhammouda B., Vazquez-Leal H. and Sarmiento-Reyes A., 2014. Modified Reduced Differential Transform Method for Partial Differential-Algebraic Equations. Journal of Applied Mathematics, 1(2014): 1-9. [03] Ben Mariem S. and Ben Mabrouk S., 2014. Drying Characteristics of Tomato Slices and Mathematical Modeling. International Journal of Energy Engineering, 4(2A): 17-24. [04] Ben Mariem S. and Ben Mabrouk S., 2015. Moisture Sorption Isotherms and Isosteric Heats of Sorption of Tomato Slices. American Journal of Renewable and Sustainable Energy, 1(3): 140-155. [05] Jin L., 2008. Homotopy perturbation method for solving partial differential equations with variable coefficients. Int. J. Contemp. Math. Sciences, (3): 1395-1407. [06] Kanzari S., Hachicha M. and Bouhlila R., 2012. Laboratory Method for Estimating Soil Water Retention Properties of an Unsaturated Soils. Walailak Journal of Science and Technology, 9(4): 361-367. [07] Kanzari S. and Ben Mariem S., 2014. One-dimensional numerical modeling for water flow and solute transport in an unsaturated soil. International Journal of Applied Science and Mathematics, 1(2): 52-56. [08] Kanzari S., Hachicha M. and Bouhlila R., 2015. Laboratory method for estimating solute transport parameters of an unsaturated soil. American Journal of Geophysics, Geochemistry and Geosystems, 1(4): 151-156. [09] Keskin and Oturanc G., 2010. Application of reduced differential transformation method for solving gas dynamics equation. Int. J. Contemp. Math. Sciences, (5): 1091- 1096. [10] Mohyud-Din S.T., 2009. Solving heat and wave-like equations using He's polynomials. Mathematical Problems in Engineering, 2009: 1-12. [11] Noor M.A. and Mohyud-Din S.T., 2008. Modified variational iteration method for heat and wave-like equations. Acta Applicandae Mathematicae, (104): 257-269. [12] Sohail M. and Mohyud-Din S.T., 2012 (a). Reduced Differential Transform Method for Time-fractional Heat Equations. International Journal of Modern Theoretical Physics, 1(1): 13-22. [13] Sohail M. and Mohyud-Din S.T., 2012 (b). Reduced Differential Transform Method for Solving a System of Fractional PDEs. International Journal of Modern Theoretical Physics, 4(1): 21-29.