### Analytical and approximate solution of two-dimensional convection-diffusion problems

#### Abstract

In this work, we have used reduced differential transform method (RDTM) to compute an approximate solution of the Two-Dimensional Convection-Diffusion equations (TDCDE). This method provides the solution quickly in the form of a convergent series. Also, by using RDTM the approximate solution of two-dimensional convection-diffusion equation is obtained. Further, we have computed exact solution of non-homogeneous CDE by using the same method. To the best of my knowledge, the research work carried out in the present paper has not been done, and is new. Examples are provided to support our work.

#### Keywords

#### Full Text:

PDF#### References

Baskonus, H.M. (2019). Complex Soliton Solutions to the Gilson-Pickering Model. Axioms, 8(1), 18.

Ilhan, O.A., Esen, A., Bulut, H., & Baskonus, H.M. (2019). Singular Solitons in the Pseudoparabolic Model Arising in Nonlinear Surface Waves. Results in Physics, 12, 17121715.

Cattani, C., Sulaiman, T.A., Baskonus, H.M., & Bulut, H. (2018). Solitons in an inhomogeneous Murnaghan’s rod. European Physical Journal Plus, 133(228), 1-12.

Baskonus, H.M., Sulaiman, T.A. & Bulut, H. (2018). Dark, bright and other optical solitons to the decoupled nonlinear Schrdinger equation arising in dual-core optical fibers. Optical and Quantum Electronics, 50(4), 1-12.

Ciancio, A., Baskonus, H.M., Sulaiman, T.A., & Bulut, H. (2018). New Structural Dynamics of Isolated Waves Via the Coupled Nonlinear Maccari’s System with Complex Structure. Indian Journal of Physics, 92(10), 12811290.

Ilhan, O.A., Sulaiman, T.A., Bulut, H., & Baskonus, H.M. (2018). On the New Wave Solutions to a Nonlinear Model Arising in Plasma Physics. European Physical Journal Plus, 133(27), 1-6.

Yel, G., Baskonus, H.M., & Bulut, H. (2017). Novel archetypes of new coupled KonnoOono equation by using sineGordon expansion method. Optical and Quantum Electronics, 49(285), 1-10.

Baskonus, H.M. (2017). New Complex and Hyperbolic Function Solutions to the Generalized Double Combined Sinh-Cosh-Gordon Equation. AIP Conference Proceedings. 1798, 1-9 (020018).

Baskonus, H.M. (2016). New acoustic wave behaviors to the DaveyStewartson equation with power-law nonlinearity arising in fluid Dynamics. Nonlinear Dynamics, 86(1), 177183.

Karaa, S., & Zhang, J. (2004). Higher order ADI method for solving unsteady convectiondiffusion problems. Journal of Computational Physics, 198, 1-9.

Tian, Z. (2011). A rational high-order compact ADI method for unsteady convectiondiffusion equations. Computer Physics Communications, 182, 649-662.

Rui, H. (2003). An alternative direction iterative method with second-order upwind scheme for convection-diffusion equations. International Journal of Computer Mathematics, 80(4), 527-533.

Mekuria, G.T., & Rao, J.A. (2016). Adaptive finite element method for steady convectiondiffusion equation. American Journal of Computational Mathematics, 6(3), 275-285.

Li, L., Jiang, Z., & Yin, Z. (2018). Fourthorder compact finite difference method for solving two-dimensional convection-diffusion equation. Advances in Difference Equations, 2018, 1-24.

Momani, S. (2008). A Decomposition Method for Solving Unsteady Convection Diffusion Problems. Turkish Journal of Mathematics, 32, 51-60.

Saqib, M., Hasnain, S., & Mashat, D.S. (2017). Computational solutions of two dimensional convection-diffusion equation using Crank Nicolson and time efficient ADI. American Journal of Computational Mathematics, 7(3), 208-227.

Ismail, H.N.A., Elbarbary, E. M. E., & Salem, G. S. E. (2004). Restrictive Taylor’s approximation for solving convectiondiffusion equation. Applied Mathematics and Computation, 147, 355-363.

Castillo, M., & Power, H. (2008). The Neumann series as a fundamental solution of the two-dimensional convection-diffusion equation with variable velocity. Journal of Engineering Mathematics, 62, 189-202.

Noye, B.J., & Tan, H.H. (1989). Finite difference methods for solving the twodimensionaladvection-diffusion equation. International Journal for Numerical Methods in Fluids, 9(1), 75-98.

Sun, H., & Li, L. (2014). A CCD-ADI method for unsteady convection-diffusion equations. Computer Physics Communications, 185, 790-797.

Kalita, J.C., Dalal, D.C., & Dass, A.K. (2002). A class of higher order compact schemes for the unsteady two-dimensional convection-diffusion equation with variable convection coefficients. International Journal for Numerical Methods in Fluids, 38, 1111-1131.

Shu, C.W. (2017). Bound-preserving high order finite volume schemes for conservation laws and convection-diffusion equations. Finite Volumes for Complex Applications VIIIMethods and Theoretical Aspects, Springer Proceedings, 3-14.

Ammi, M.R.S., & Jamiai, I. (2017). Finite difference and Legendre spectral method for a time-fractional diffusion-convection equation for image restoration. Discrete & Continuous Dynamical Systems, 11(1), 103-117.

Koley, U., Risebro, N.H., Schwab, C., et al.(2017). A multilevel monte carlo finite difference method for random scalar degenerate convection-diffusion equations. Journal of Hyperbolic Differential Equations, 14(3), 415-454.

Keskin, Y. (2010). Solving partial differential equations by the reduced differential transform method. PhD Thesis. Selcuk University.

Ziqan, A.M., Armiti, S., & Suwan, L. (2016). Solving three-dimensional volterra integral equation by the reduced differential transform method. International Journal of Applied Mathematical Research, 5(2), 103-106.

DOI: http://dx.doi.org/10.11121/ijocta.01.2020.00781

### Refbacks

- There are currently no refbacks.

Copyright (c) 2020 Hatıra GÜNERHAN

This work is licensed under a Creative Commons Attribution 4.0 International License.