NUMERICAL SOLUTION FOR NONLINEAR BURGERS’ EQUATION WITH SOURCE TERM

Main Article Content

Falade Kazeem Iyanda
Bello Kareem Akanbi
Nuru Muazu

Abstract

In this paper, we formulate a four step computational algorithm to solve nonlinear Burger’s equation with source terms whose occur in aerodynamics engineering which play a major roles in convection and diffusion whose present in viscous fluid flow engineering problems. Numerical assessment  was carried out to study effect of source term  which represents the heat released in the boundary layer. Increase the source  term and decrease in  kinematic viscosity which play a major roles in obtaing velocity . Eventually, we subject the nonlinear Burger’s equation with source terms to initial and boundary conditions available in the literature. The results revealed that the new algorithm is capable and realiable to solve similar nonlinear partial differential equations occur in applied physics and engineering.

Article Details

How to Cite
Iyanda, F. K. ., Akanbi, B. K. ., & Muazu, N. . (2021). NUMERICAL SOLUTION FOR NONLINEAR BURGERS’ EQUATION WITH SOURCE TERM. American International Journal of Sciences and Engineering Research, 4(1), 53–65. https://doi.org/10.46545/aijser.v4i1.232
Section
Articles
Author Biographies

Falade Kazeem Iyanda, Kano University of Science and Technology, Nigeria

Department of Mathematics

Faculty of Computing and Mathematical Sciences

Kano University of Science and Technology, Wudil, P.M.B 3244, Kano State, Nigeria

Bello Kareem Akanbi, University of Ilorin, Nigeria

Department of Mathematics

Faculty of Physical Sciences, University of Ilorin

P.M.B.1515, Ilorin, Kwara State, Nigeria

Nuru Muazu, Kano University of Science and Technology, Nigeria

Department of Mathematics

Faculty of Computing and Mathematical Sciences

Kano University of Science and Technology, Wudil, P.M.B 3244, Kano State, Nigeria

References

Abdou, M. A., & Soliman, A. A. (2005). Variational iteration method for solving Burger's and coupled Burger's equations. Journal of computational and Applied Mathematics, 181(2), 245-251.

Burgers, J. M. (1948). A mathematical model illustrating the theory of turbulence. In Advances in applied mechanics (Vol. 1, pp. 171-199). Elsevier.

Burgers, J.M. (1939). Trans. R. Netherlands Acad. Sci. Amster-dam, 17, 1.

Chandrasekharan Nair, L., & Awasthi, A. (2019). Quintic trigonometric spline based numerical scheme for nonlinear modified Burgers' equation. Numerical Methods for Partial Differential Equations, 35(3), 1269-1289.

Desai, K. R., & Pradhan, V. H. (2012). Solution of Burger’s equation and coupled Burger’s equations by Homotopy perturbation method. International Journal of Engineering Research and Applications, 2(3), 2033-2040.

Falade, K. I., & Tiamiyu, A.T. (2020). Numerical solution of partial differential equations with fractional variable coefficients using new iterative method (NIM), I.J. Mathematical Sciences and Computing, 3, 12-21.

Ismail, H. N., Raslan, K., & Abd Rabboh, A. A. (2004). Adomian decomposition method for Burger's–Huxley and Burger's–Fisher equations. Applied mathematics and computation, 159(1), 291-301.

Mayur, P. A., Lakshmı, C., Vıjıtha, M. & Aswın, V.S. (2018). A systematic literature review of Burgers’ equation with recent advances, Pramana – J. Phys, 69.

Mittal, R., & Jain, R. (2021). Solving Burgers’ equation based on collocation of the modified cubic B-splines over finite elements, Appl. Math. Comput, 218, 7839.

Mohamed, N.A. (2019). Solving one- and two-dimensional unsteady Burgers’ equation using fully implicit finite difference schemes, Arab journal of basıc and applıed scıences, 26(1), 254–268.

Nieuwstadt, F. T., & Steketee, J. A. (Eds.). (2012). Selected papers of JM Burgers. Springer Science & Business Media.

Panayotounakos, D. E., & Drikakis, D. (1995). On the closed‐form solutions of the wave, diffusion and Burgers equations in fluid mechanics. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 75(6), 437-447.