TY - JOUR T1 - Numerical approach of fisher's equation with strang splitting technique using finite element galerkin method AU - Karta, Melike PY - 2023 DA - April JF - Sigma Journal of Engineering and Natural Sciences JO - SIGMA PB - Yildiz Technical University WT - DergiPark SN - 1304-7191 SP - 344 EP - 355 VL - 41 IS - 2 LA - en AB - In the present paper, non-linear Fisher’s reaction-diffusion equation is solved numerically by using Strang splitting technique with the help of Galerkin method combined with quadratic B-spline base functions. For this aim, Fisher’s equation is split into two sub-equations with respect to time such that one is linear and the other one is nonlinear. Galerkin method using quadratic B-spline finite elements is applied to each sub-equation. To check the correctness and reliability of the presented approach, we have realized on three numerical examples and have made a comparison with earlier studies existing in the literature calculating the error norms norms 𝐿2 π‘Žπ‘›π‘‘ 𝐿∞ .The solutions obtained in the article show that the present method is quite proper for using many partial differential equations in terms of being easy and conve-nient to computer application. KW - Symmetric Strang Splitting KW - Reaction-Diffusion Equation KW - Quadratik B-Splines KW - Finete Element Method CR - REFERENCES CR - [1] Qureshi S, Yusuf A, Aziz S. Fractional numerical dynamics for the logistic population growth model under Conformable Caputo: a case study with real observations. Phys Scr 2021;96:114002. [CrossRef] CR - [2] Memon Z, Qureshi S, Memon BR. Assessing the role of quarantine and isolation as control strategies faor COVID-19 outbreak: a case study. Chaos Solit Fractals 2021;144:110655. [CrossRef] CR - [3] Qureshi S, Yusuf A. Fractional derivatives applied to MSEIR problems: Comparative study with real world data. Eur Phys J Plus 2019;134:1βˆ’13. [CrossRef] CR - [4] Qureshi S, Fractal-fractional differentiation for the modeling and mathematical analysis of non- lin-ear diarrhea transmission dynamics under the use of real data. Chaos Solit Fractals 2020;136:109812.[CrossRef] CR - [5] Fisher RA. The wave of advance of advantageous genes. Ann Eugen 1936;7:355βˆ’369. [CrossRef] CR - [6] Kolmogorov A, Petrovskii I, Piskunov N. Study of a diffusion equation that Δ±s related to the growth of a quality of matter and Δ±ts application to a biological problem. Moscow Univ Mathem Bull 1937;1:1βˆ’26. CR - [7] Canosa J. On a nonlinear diffusion equation describ-ing population growth. J Res Dev 1973;17:307βˆ’313.[CrossRef] CR - [8] Gazdag J, Canosa J. Numerical solution of Fisher's equation. J Appl Prob 1974;11:445βˆ’457. [CrossRef] CR - [9] Tang S, Weber RO. Numerical study of Fisher's equa-tion by a Petrov-Galerkin finite element method. J Austral Math Soc Ser B 1991;33:27βˆ’38. [CrossRef] [10] Qiu Y, Sloan DM. Numerical solution of Fisher's equation using a moving mesh method. J Comput Phys 1998;146:726βˆ’746. [CrossRef] CR - [11] Zhao S, Wei GW. Comparison of the discrete sin-gular convolution and three other numerical schemes for solving Fisher's equation. J Sci Comput 2003;25:127βˆ’147. [CrossRef] CR - [12] Cattani C, Kudreyko A. Mutiscale analysis of the fisher equation. Lect Notes Comput Sci 2008;5072: 1171βˆ’1180. [CrossRef] CR - [13] Mittal RC, Arora G. Efficient numerical solution of Fisher's equation by using B-spline method. Int. J Comput Math 2010;87:3039βˆ’3051. [CrossRef] CR - [14] Dagg II, Sahin A, Korkmaz A. Numerical investigation of the solution of Fisher's equation via the B- spline Galerkin method. Numer Methods Partial Differ Equ 2010;26:1483βˆ’1503. [CrossRef] CR - [15] Mittal RC, Jain R. Cubic B-splines collocation method for solving nonlinear parabolic partial dif-ferential equations with Neumann boundary con-ditions. commun Nonlinear sci. Numer.Simulat 2012;17:4616βˆ’4625. [CrossRef] CR - [16] Mittal RC, Jain RK. Numerical solutions of nonlinear Fisher's reaction-diffusion equation with mod-ified cubic B- spline collocation method. Math Sci 2013;7:1βˆ’10. [CrossRef] CR - [17] Sahin A, Dagg II, Saka B. A B-spline algorithm for the numerical solution of Fisher's equation. Kybernetes 2008;37:326βˆ’342. [CrossRef] CR - [18] Sahin A, Ozmen O. Usage of higher order B-splines in numerical solution of Fishers equation. Int J Nonlinear Sci 2014;17:241βˆ’253. CR - [19] Ersoy O, Dagg I.. The extended B-spline collocation method for numerical solutions of Fishers equation. AIP Conf Proc 2015;1648:370011. [CrossRef] CR - [20] Dag I, Ersoy O. The exponential cubic B-spline algorithm for Fisher equation. Chaos Solit Fractals 2016;86:101βˆ’106. [CrossRef] CR - [21] Rohila R, Mittal R.C. Numerical study of reac-tion diffusion Fisher's equation by fourth order cubic B-spline collocation method. Math Sci 2018;12:79βˆ’89. [CrossRef] CR - [22] Tamsir M, Srivastava VK, Dhiman N, Chauhan A. Numerical computation of nonlinear fisher's reac-tion-diffusion equation with exponential modified cubic b-spline differential quadrature method. Int. J Appl Comput Math 2018;4:1βˆ’13. [CrossRef] CR - [23] Dhiman N, Chauhan A, Tamsir M, Chauhan A. Numerical simulation of Fisher's type equation via a collocation technique based on re-defined quintic B-splines. Multidiscip Model Mater Struct 2020;16:1117βˆ’1130. [CrossRef] CR - [24] Kapoor M, Joshi V. Solution of non-linear Fisher's reaction-diffusion equation by using Hyperbolic B-spline based differential quadrature method. J Phys Conf Ser 2020;1531:012064. [CrossRef] CR - [25] Madzvamuse A. Time stepping schemes for moving grid finite elements applied to reaction- diffusion systems on fixed and growing domains. J Comput Phys 2006;214:239βˆ’263. [CrossRef] CR - [26] Hundsdorfer W, Verwer J. Numerical solution of time-dependent advection-diffusion- reaction equations . 1st ed. Berlin: Springer; 2003. [CrossRef] CR - [27] Seydaogglu M, Blanes S. High-order splitting meth-ods for separable non-autonomous parabolic equa-tions. Appl Numer Math 2014;84:22βˆ’32. [CrossRef] CR - [28] Strang G. On the construction and comparison of difference schemes. J Numer Anal 1968;5:506βˆ’517.[CrossRef] UR - https://dergipark.org.tr/en/pub/sigma/issue//1403523 L1 - https://dergipark.org.tr/en/download/article-file/3593598 ER -