A Hybrid Differential Transforms and Finite Difference Method to Numerical Solution of Convection–Diffusion Equation
Keywords:
Hybrid method, Differential transform, Finite difference method, Convection–Diffusion equationAbstract
In this work, we discuss a hybrid-based method on differential transforms and a finite difference method to numerical solution of convection–diffusion equation with Dirichlet’s type boundary conditions. The developed method is tested on various problems and the numerical results are reported in tabular and figure form. This method can be easily extended to handle non-linear convection–diffusion partial differential equations.
Downloads
References
M. Dehghan, Weighted finite difference techniques for the one-dimensional advection–diffusion equation, Appl. Math. Comput. 147 (2004) 307–319.
A. Mohebbi, M. Dehghan, High-order compact solution of the one-dimensional heat and advection–diffusion equations, Appl. Math. Model. 34 (2010) 3071–3084.
D.K. Salkuyeh, On the finite difference approximation to the convection–diffusion equation, Appl. Math. Comput. 179 (2006) 79-86.
Hossein Aminikhah, Javad Alavi, Numerical Solution of Convection–Diffusion Equation Using Cubic B-Spline Quasi-Interpolation, Thai Journal of Mathematics, 14(3) (2015), 599-613.
H.N.A. Ismail, E.M.E. Elbarbary, G.S.E. Salem, Restrictive Taylor’s approximation for solving convection–diffusion equation, Appl. Math. Comput. 147 (2004) 355–363.
Mohan K. Kadalbajoo, Lok Pati Tripathi , Alpesh Kumar, A cubic B-spline collocation method for a numerical solution of the generalized Black–Scholes equation, Mathematical and Computer Modelling 55 (2012) 1483–1505.
Joan Goh, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, A quartic B-spline for second-order singular boundary value problems, Computers & Mathematics with Applications 64 (2012) 115–120.
S.A. Khuri , A. Sayfy, A spline collocation approach for a generalized parabolic problem subject to non-classical conditions ,Applied Mathematics and Computation 218 (2012) 9187–9196.
Hsin-Ping Chu, Chieh-Li Chen, Hybrid differential transform and finite difference method to solve the nonlinear heat conduction problem, Communications in Nonlinear Science and Numerical Simulation, 13 (2008) 1605-1614.
Huan-Sen Peng, Chieh-Li Chen, Hybrid differential transformation and finite difference method to annular fin with temperature-dependent thermal conductivity, International Journal of Heat and Mass Transfer, 54 (2011) 2427-2433.
Huan-Sen Peng and Chieh-Li Chen, Application of hybrid differential transformation and finite difference method on the laser heating problem, Numerical Heat Transfer, Part A, 59 (2011) 28-42.
Inci Çilingir Süngü, Hüseyin Demir, Application of the hybrid differential transform method to the nonlinear equations, Applied Mathematics, 3 (2012) 246-250
R.C.Mittal, R.K.Jain, Redefined cubic B-splines collocation method for solving convection-diffusion equations, Applied Mathematical Modelling, 36 (2012) 5555-5573.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.