RDTM ile Singüler Pertürbe Burger-Huxley Denkleminin Yaklaşık Çözümü

Bu çalışmada, singuler pertürbe Burger-Huxley kısmi türevli diferansiyel denklemini çözmek için indirgenmiş diferansiyel dönüşüm yöntemi (RDTM) önerilmiştir. İlk olarak bu denklem cebirsel denkleme dönüştürülür. Daha sonar tekrarlama bağıntısı ve diferansiyel dönüşüm katsayıları elde edilir. Son olarak, üç örnek için bu denklemin oldukça doğru yaklaşık çözümleri bulunur.

The Approximate Solution of Singularly Perturbed Burger-Huxley Equation with RDTM

In this study, reduced differential transform method (RDTM) is proposed to solve singularly perturbed Burger- Huxley partial differential equation. Firstly, this equation is transformed to algebraic equation. Then, recurrence relation and differential transform coefficients are obtained. Finally, highly accurate approximate solutions of this equation are found for three examples.

PDF

___

[1] Abazari R., Abazari N. 2013. Numerical Study of Burgers–Huxley Equations via Reduced Differential Transform Method. Comp. Appl. Math., 32 (1): 1-17.
[2] Az-Zo'bi E.A. 2014. On the Reduced Differential Transform Method and its Application to the Generalized Burgers-Huxley Equation. Applied Mathematical Sciences, 8 (177): 8823-8831.
[3] Hashim I., Noorani M.S.M., Batiha B. 2006. A note on the Adomian Decomposition Method for the Generalized Huxley Equation. Applied Mathematics and Computation, 181: 1439–1445.
[4] Ismail H.N.A., Raslan K., Abd Rabboh A.A. 2004. Adomian Decomposition Method for Burger’s–Huxley and Burger’s–Fisher Equations. Applied Mathematics and Computation, 159: 291-301.
[5] Liu L-B., Liang Y., Zhang J. 2020. A Robust Adaptive Grid Method for Singularly Perturbed Burger-Huxley Equations. Electronic Research Archive, 28 (4): 1439-1457.
[6] Hashemi M.S., Baleanu D., Barghi H. 2016. Singularly perturbed Burgers-Huxley Equation by a Meshless Method. Thermal Science, 21 (6): 2689-2698.
[7] Yefımova O.Y., Kudryashov N.A. 2004. Exact Solutions of the Burgers-Huxley Equation. J. Appl. Maths. Mechs., 68 (3): 413-420.
[8] Appadu A.R., Inan B., Olatunji Tijani Y. 2019. Comparative Study of Some Numerical Methods for the Burgers–Huxley Equation. Symmetry, 11 (11).
[9] Burgers J.M. 1948. A Mathematical Model Illustrating the Theory of Turbulence. Advances in Applied Mechanics, Academic Press, New York, 171-199.
[10] Satsuma J. 1987. Topics in Soliton Theory and Exactly Solvable Nonlinear Equations. World Scientific, Singapore.
[11] Bateman H. 1915. Some Recent Researches on the Motion of Fluids. Monthly Weather Review, 43: 63-170.
[12] Chen C.K., Ho S.H. 1999. Solving Partial Differential Equations by Two Dimensional Differential Transform. Appl. Math. Comput., 106: 171-179.
[13] Zhou J.K. 1986. Differential Transform and Its Application for Electrical Circuits. Huazhong University Press, Wuhan.
[14] Ayaz F. 2004. Applications of Differential Transform Method to Differential-Algebraic Equations. Applied Mathematics and Computation, 152: 649-657.
[15] Arslan D. 2020. The Comparison Study of the Hybrid Method with RDTM for Solving Rosenau- Hyman Equation. Applied mathematics and Nonlinear science, 5 (1): 267-274.
[16] Arslan D. 2019. A Novel Hybrid Method for Singularly Perturbed Delay Differential Equations. Gazi University Journal of Science, 32 (1): 217-223.
[17] Nayfeh A.H. 1993. Introduction to Perturbation Techniques. Wiley, New York.
[18] Arslan D. 2019. Approximate Solutions of Singularly Perturbed Nonlinear Ill-posed and Sixth- order Boussinesq Equations with Hybrid Method. BEU Journal of Science, 8 (2): 451-458.
[19] Arslan D. 2020. Numerical Solution of Nonlinear the Foam Drainage Equation via Hybrid Method. New Trends in Mathematical Sciences, 8 (1): 50-57.
[20] Ayaz F. 2003. On the Two Dimensional Differential Transform Method. Appl. Math. Comput, 143: 361-374.
[21] Gupta V., Kadalbajoo M.K. 2011. A Singular Perturbation Approach to Solve Burgers-Huxley Equation via Monotone Finite Difference Scheme on Layer-Adaptive Mesh. Commun. Nonlinear Sci. Numer. Simulat., 16: 1825-1844.
[22] İnan B., Bahadır A.R. 2015. Numerical Solutions of the Generalized Burgers-Huxley Equation by Implicit Exponential Finite Difference Method. Journal of Applied Mathematics, Statistic and Informatics, 11: 57-67.
[23] Çiçek Y., Tanoğlu G. 2016. Strang Splitting Method for Burgers-Huxley Equation. Applied Mathematics and Computation, 276: 454-467.
[24] Bulut H., Baskonus, H.M., Pandir Y. 2013. The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation. Abstract and Applied Analysis, 2013: 8 pages,