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Journal articles on the topic 'Fisher's equation'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Phillips, Peter C. B. "Econometric Analysis of Fisher's Equation." American Journal of Economics and Sociology 64, no. 1 (2005): 125–68. http://dx.doi.org/10.1111/j.1536-7150.2005.00355.x.

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2

Cavazzoni, R. "Diffusive approximation of fisher's equation." Computers & Mathematics with Applications 39, no. 9-10 (2000): 101–14. http://dx.doi.org/10.1016/s0898-1221(00)00090-0.

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3

Broadbridge, P., B. H. Bradshaw, G. R. Fulford, and G. K. Aldis. "Huxley and Fisher equations for gene propagation: An exact solution." ANZIAM Journal 44, no. 1 (2002): 11–20. http://dx.doi.org/10.1017/s1446181100007860.

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AbstractThe derivation of gene-transport equations is re-examined. Fisher's assumptions for a sexually reproducing species lead to a Huxley reaction-diffusion equation, with cubic logistic source term for the gene frequency of a mutant advantageous recessive gene. Fisher's equation more accurately represents the spread of an advantaged mutant strain within an asexual species. When the total population density is not uniform, these reaction-diffusion equations take on an additional non-uniform convection term. Cubic source terms of the Huxley or Fitzhugh-Nagumo type allow special nonclassical s

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4

Jovanoski, Zlatko, and G. Robinson. "Piecewise linear approximation to Fisher's equation." ANZIAM Journal 53 (August 5, 2012): 465. http://dx.doi.org/10.21914/anziamj.v53i0.5129.

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5

Liu, Yong. "ON FISHER'S EQUATION WITH A PARAMETER." Acta Mathematica Scientia 9, no. 3 (1989): 241–55. http://dx.doi.org/10.1016/s0252-9602(18)30350-3.

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6

Zhou, X.-W. "Exp-function method for solving Fisher's equation." Journal of Physics: Conference Series 96 (February 1, 2008): 012063. http://dx.doi.org/10.1088/1742-6596/96/1/012063.

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7

Rohrhofer, Franz Martin, Stefan Posch, Clemens Gößnitzer, and Bernhard Geiger. "Approximating families of sharp solutions to Fisher's equation with physics-informed neural networks." Computer Physics Communications 307 (November 6, 2024): 109422. https://doi.org/10.1016/j.cpc.2024.109422.

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This paper employs physics-informed neural networks (PINNs) to solve Fisher's equation, a fundamental reaction-diffusion system with both simplicity and significance. The focus is on investigating Fisher's equation under conditions of large reaction rate coefficients, where solutions exhibit steep traveling waves that often present challenges for traditional numerical methods. To address these challenges, a residual weighting scheme is introduced in the network training to mitigate the difficulties associated with standard PINN approaches. Additionally, a specialized network architecture desig

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8

Usman, Muhammad, Hidayat Ullah Khan, Zareen A. Khan, and Hussam Alrabaiah. "Study of nonlinear generalized Fisher equation under fractional fuzzy concept." AIMS Mathematics 8, no. 7 (2023): 16479–93. http://dx.doi.org/10.3934/math.2023842.

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<abstract><p>Fractional calculus can provide an accurate model of many dynamical systems, which leads to a set of partial differential equations (PDE). Fisher's equation is one of these PDEs. This article focuses on a new method that is used for the analytical solution of Fuzzy nonlinear time fractional generalized Fisher's equation (FNLTFGFE) with a source term. While the uncertainty is considered in the initial condition, the proposed technique supports the process of the solution commencing from the parametric form (double parametric form) of a fuzzy number. Next, a joint mechan

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9

Dhiman, Neeraj, Amit Chauhan, Mohammad Tamsir, and Anand Chauhan. "Numerical simulation of Fisher's type equation via a collocation technique based on re-defined quintic B-splines." Multidiscipline Modeling in Materials and Structures 16, no. 5 (2020): 1117–30. http://dx.doi.org/10.1108/mmms-09-2019-0166.

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PurposeA collocation technique based on re-defined quintic B-splines over Crank-Nicolson is presented to solve the Fisher's type equation. We take three cases of aforesaid equation. The stability analysis and rate of convergence are also done.Design/methodology/approachThe quintic B-splines are re-defined which are used for space integration. Taylor series expansion is applied for linearization of the nonlinear terms. The discretization of the problem gives up linear system of equations. A Gaussian elimination method is used to solve these systems.FindingsThree examples are taken for analysis.

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10

Agom, E. U., F. O. Ogunfiditimi, E. V. Bassey, and C. Igiri. "REACTION-DIFFUSION FISHER’S EQUATIONS VIA DECOMPOSITION METHOD." Journal of Computer Science and Applied Mathematics 5, no. 2 (2023): 145–53. http://dx.doi.org/10.37418/jcsam.5.2.7.

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The effect of the source, initial or boundary conditions in the use of Adomian decomposition method (ADM) on nonlinear partial differential equation or nonlinear equation in general is enormous. Sometimes the equation in question result to continuous exact solution in series form, other times it result to discrete approximate analytical solutions. In this paper, we show that continuous exact solitons can be obtained on application of ADM to the Fisher's equation with the deployment Taylor theorem to the terms(s) in question. And, the resulting series is split into the integral equations during

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11

Rao, A. M., A. S. Warke, A. H. Agadi, and G. A. Birajdar. "LAPLACE DECOMPOSITION METHOD FOR NONLINEAR BURGER'S-FISHER'S EQUATION." Advances in Mathematics: Scientific Journal 9, no. 3 (2020): 1163–80. http://dx.doi.org/10.37418/amsj.9.3.60.

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12

Witelski, T. P. "Merging traveling waves for the porous-Fisher's equation." Applied Mathematics Letters 8, no. 4 (1995): 57–62. http://dx.doi.org/10.1016/0893-9659(95)00047-t.

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13

Olmos, Daniel, and Bernie D. Shizgal. "A pseudospectral method of solution of Fisher's equation." Journal of Computational and Applied Mathematics 193, no. 1 (2006): 219–42. http://dx.doi.org/10.1016/j.cam.2005.06.028.

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14

Mavoungou, T., and Y. Cherruault. "Numerical study of fisher's equation by Adomian's method." Mathematical and Computer Modelling 19, no. 1 (1994): 89–95. http://dx.doi.org/10.1016/0895-7177(94)90118-x.

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15

Abur-Robb, M. F. K. "Explicit solutions of Fisher's equation with three zeros." International Journal of Mathematics and Mathematical Sciences 13, no. 3 (1990): 617–20. http://dx.doi.org/10.1155/s0161171290000862.

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Explicit traveling wave solutions of Fisher's equation with three simple zerosut=uxx+u(1−u)(u−a),a∈(0,1), are obtained for the wave speedsC=±2(12−a)suggested by pure analytic considerations. Two types of solutions are obtained: one type is of a permanent wave form whereas the other is not.

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16

Motsa, S. S., V. M. Magagula, and P. Sibanda. "A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations." Scientific World Journal 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/581987.

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This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accu

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17

Roman-Miller, Lance, and Philip Broadbridge. "Exact Integration of Reduced Fisher's Equation, Reduced Blasius Equation, and the Lorenz Model." Journal of Mathematical Analysis and Applications 251, no. 1 (2000): 65–83. http://dx.doi.org/10.1006/jmaa.2000.7020.

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18

Myrzakhmetova, B., U. Besterekov, I. Petropavlovsky, S. Ahnazarova, V. Kiselev, and S. Romanova. "Optimization of Decomposition Process of Karatau Phosphorites." Eurasian Chemico-Technological Journal 14, no. 2 (2012): 183. http://dx.doi.org/10.18321/ectj113.

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Phosphorous-acid process of Karatau phosphorites’ decomposition has been studied. The impact of temperature, time and acid rate on decomposition process of phosphate raw material, the conditions ensuring maximum degree of phosphorite decomposition have been identified. Variance estimate of experiment results’ reproducibility has been carried out by mathematical statistics method; the coefficients of regression equations have been set. The significance of regression equation coefficients has been checked up by Student’s criterion, and the adequacy of regression equation to experiment has been c

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19

Hussain, E. A., and Z. M. Alwan. "The finite volume method for solving Buckmaster's equation, Fisher's equation and sine Gordon's equation for PDE's." International Mathematical Forum 8 (2013): 599–617. http://dx.doi.org/10.12988/imf.2013.13063.

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20

Dhumal, M. L., and S. B. Kiwne. "Numerical Treatment of Fisher's Equation using Finite Difference Method." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 37e, no. 1 (2018): 94. http://dx.doi.org/10.5958/2320-3226.2018.00010.3.

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21

Mittal, R. C., and Sumit Kumar. "Numerical study of Fisher's equation by wavelet Galerkin method." International Journal of Computer Mathematics 83, no. 3 (2006): 287–98. http://dx.doi.org/10.1080/00207160600717758.

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22

El-Danaf, Talaat S., and Adel R. Hadhoud. "Computational method for solving space fractional Fisher's nonlinear equation." Mathematical Methods in the Applied Sciences 37, no. 5 (2013): 657–62. http://dx.doi.org/10.1002/mma.2822.

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23

Secer, Aydin, and Melih Cinar. "A Jacobi wavelet collocation method for fractional fisher's equation in time." Thermal Science 24, Suppl. 1 (2020): 119–29. http://dx.doi.org/10.2298/tsci20119s.

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In this study, the Jacobi wavelet collocation method is studied to derive a solution of the time-fractional Fisher?s equation in Caputo sense. Jacobi wavelets can be considered as a generalization of the wavelets since the Gegenbauer, and thus also Chebyshev and Legendre polynomials are a special type of the Jacobi polynomials. So, more accurate and fast convergence solutions can be possible for some kind of problems thanks to Jacobi wavelets. After applying the proposed method to the considered equation and discretizing the equation at the collocation points, an algebraic equation system is d

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24

Secer, Aydin, and Melih Cinar. "A Jacobi wavelet collocation method for fractional fisher's equation in time." Thermal Science 24, Suppl. 1 (2020): 119–29. http://dx.doi.org/10.2298/tsci20s1119s.

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In this study, the Jacobi wavelet collocation method is studied to derive a solution of the time-fractional Fisher?s equation in Caputo sense. Jacobi wavelets can be considered as a generalization of the wavelets since the Gegenbauer, and thus also Chebyshev and Legendre polynomials are a special type of the Jacobi polynomials. So, more accurate and fast convergence solutions can be possible for some kind of problems thanks to Jacobi wavelets. After applying the proposed method to the considered equation and discretizing the equation at the collocation points, an algebraic equation system is d

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25

Lui, Roger. "Existence and stability of travelling wave solutions for an evolutionary ecology model." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 115, no. 1-2 (1990): 1–18. http://dx.doi.org/10.1017/s0308210500024525.

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SynopsisMonotone travelling wave solutions are known to exist for Fisher's equation which models the propagation of an advantageous gene in a single locus, two alleles population genetics model. Fisher's equation assumed that the population size is a constant and that the fitnesses of the individuals in the population depend only on their genotypes. In this paper, we relax these assumptions and allow the fitnesses to depend also on the population size. Under certain assumptions, we prove that in the second heterozygote intermediate case, there exists a constant θ*>0 such that monotone trave

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26

Dimand, Robert W., and Rebeca Gomez Betancourt. "Retrospectives Irving Fisher's Appreciation and Interest (1896) and the Fisher Relation." Journal of Economic Perspectives 26, no. 4 (2012): 185–96. http://dx.doi.org/10.1257/jep.26.4.185.

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Irving Fisher's monograph Appreciation and Interest (1896) proposed his famous equation showing expected inflation as the difference between nominal interest and real interest rates. In addition, he drew attention to insightful remarks and numerical examples scattered through the earlier literature, and he derived results ranging from the uncovered interest arbitrage parity condition between currencies to the expectations theory of the term structure of interest rates. As J. Bradford DeLong wrote in this journal (Winter 2000), “The story of 20th century macroeconomics begins with Irving Fisher

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27

Queller, David C. "The gene's eye view, the Gouldian knot, Fisherian swords and the causes of selection." Philosophical Transactions of the Royal Society B: Biological Sciences 375, no. 1797 (2020): 20190354. http://dx.doi.org/10.1098/rstb.2019.0354.

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The biological units-of-selection debate has centred on questions of which units experience selection and adaptation. Here, I use a causal framework and the Price equation to develop the gene's eye perspective. Genes are causally special in being both replicators and interactors. Gene effects are tied together in a complex Gouldian knot of interactions, but Fisher deployed three swords to try to cut the knot. The first, Fisher's average excess, is non-causal, so not fully satisfactory in that respect. The Price equation highlights Fisher's other two swords, choosing to model only selection, an

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28

VILLANI, C. "DECREASE OF THE FISHER INFORMATION FOR SOLUTIONS OF THE SPATIALLY HOMOGENEOUS LANDAU EQUATION WITH MAXWELLIAN MOLECULES." Mathematical Models and Methods in Applied Sciences 10, no. 02 (2000): 153–61. http://dx.doi.org/10.1142/s0218202500000100.

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We give a direct proof of the fact that, in any dimension of the velocity space, Fisher's quantity of information is nonincreasing with time along solutions of the spatially homogeneous Landau equation for Maxwellian molecules. This property, which was first seen in numerical simulation in plasma physics, is linked with the theory of the spatially homogeneous Boltzmann equation.

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29

Bezekçi, Burhan. "The Refined Physics-Informed Neural Networks for Nonlinear Convection-Reaction-Diffusion Equations Using Exponential Schemes." Black Sea Journal of Engineering and Science 8, no. 4 (2025): 7–8. https://doi.org/10.34248/bsengineering.1645207.

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The nonlinear convection-reaction-diffusion equations model complex real-world phenomena across scientific and engineering disciplines. However, solving these equations analytically is often impossible due to their nonlinear nature. As a result, researchers have turned to numerical and computational methods to find approximate solutions. These methods, while effective, can struggle with issues such as stability, accuracy, and the ability to handle sharp gradients or complex interactions between convection, diffusion, and reaction terms. To address these challenges, this work introduces an enha

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30

Nardini, John T., and D. M. Bortz. "Investigation of a Structured Fisher's Equation with Applications in Biochemistry." SIAM Journal on Applied Mathematics 78, no. 3 (2018): 1712–36. http://dx.doi.org/10.1137/16m1108546.

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31

Wang, Zhenli, Lihua Zhang, and Hanze Liu. "LIE SYMMETRY ANALYSIS TO FISHER'S EQUATION WITH TIME FRACTIONAL ORDER." Journal of Applied Analysis & Computation 10, no. 5 (2020): 2058–67. http://dx.doi.org/10.11948/20190323.

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32

Carey, G. F., and Yun Shen. "Least-squares finite element approximation of Fisher's reaction-diffusion equation." Numerical Methods for Partial Differential Equations 11, no. 2 (1995): 175–86. http://dx.doi.org/10.1002/num.1690110206.

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33

Qiu, Y., and D. M. Sloan. "Numerical Solution of Fisher's Equation Using a Moving Mesh Method." Journal of Computational Physics 146, no. 2 (1998): 726–46. http://dx.doi.org/10.1006/jcph.1998.6081.

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34

Watt, S. D., and R. O. Weber. "Reaction waves and non-constant diffusivities." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 37, no. 4 (1996): 458–73. http://dx.doi.org/10.1017/s0334270000010808.

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AbstractA reaction-diffusion equation with non-constant diffusivity,ut = (D(x, t)ux)x + F(u),is studied for D(x, t) a continuous function. The conditions under which the equation can be reduced to an equivalent constant diffusion equation are derived. Some exact forms for D(x, t) are given. For D(x, t) a stochastic function, an explicit finite difference method is used to numerically determine the effect of randomness in D(x, t) upon the speed of the reaction wave solution to Fisher's equation. The extension to two spatial dimensions is considered.

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35

Ahmadjanov, Suhrob. "DESIGN OF MECHANICAL PROPERTIES OF WIND FABRIC." International Journal of Advance Scientific Research 4, no. 6 (2024): 30–39. http://dx.doi.org/10.37547/ijasr-04-06-06.

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In the article, among the main properties of the fabric, the fiber composition of the hemlock thread, the thickness of the hemlock thread, and changes in the density of the hemlock thread in the fabric are analyzed as factors affecting it. Using mathematical modeling methods, regression equations were obtained to calculate the tensile strength of the tissue. The coefficients of the regression equation were tested by Student's and the equation by Fisher's test. Cotton and polyester fibers were used as the fiber content of the hemp yarns used in weaving. 100 percent polyester yarn used as a yarn

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36

Sadigh Behzadi, Sh. "Convergence of Iterative Methods Applied to Generalized Fisher Equation." International Journal of Differential Equations 2010 (2010): 1–16. http://dx.doi.org/10.1155/2010/254675.

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A generalized Fisher's equation is solved by using the modified Adomian decomposition method (MADM), variational iteration method (VIM), homotopy analysis method (HAM), and modified homotopy perturbation method (MHPM). The approximation solution of this equation is calculated in the form of series whose components are computed easily. The existence, uniqueness, and convergence of the proposed methods are proved. Numerical example is studied to demonstrate the accuracy of the present methods.

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37

Jiao, Yu-Jian, Tian-Jun Wang, and Qiong Zhang. "A Fully Discrete Spectral Method for Fisher’s Equation on the Whole Line." East Asian Journal on Applied Mathematics 6, no. 4 (2016): 400–415. http://dx.doi.org/10.4208/eajam.310315.120716a.

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AbstractA generalised Hermite spectral method for Fisher's equation in genetics with different asymptotic solution behaviour at infinities is proposed, involving a fully discrete scheme using a second order finite difference approximation in the time. The convergence and stability of the scheme are analysed, and some numerical results demonstrate its efficiency and substantiate our theoretical analysis.

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38

Frank, Steven A. "The Price Equation, Fisher's Fundamental Theorem, Kin Selection, and Causal Analysis." Evolution 51, no. 6 (1997): 1712. http://dx.doi.org/10.2307/2410995.

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39

MOSTAFA, M. A. ATALLAH, M. I. EL-HASSANI RABAB, and F. TAKI EL DIN RAMY. "SOLVING FISHER'S EQUATION USING MODIFIED EXPONENTIAL CUBIC B-SPLINE DIFFERENTIAL QUADRATURE." i-manager’s Journal on Mathematics 9, no. 2 (2020): 8. http://dx.doi.org/10.26634/jmat.9.2.17941.

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40

Mohamed, Mohamed S., Khaled A. Gepreel, and S. M. Abo-Dahab. "Optimal Homotopy Anaylsis Method for Nonlinear Partial Fractional Differential Fisher's Equation." Journal of Computational and Theoretical Nanoscience 12, no. 6 (2015): 965–70. http://dx.doi.org/10.1166/jctn.2015.3836.

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41

Mittal, R. C., and Geeta Arora. "Efficient numerical solution of Fisher's equation by using B-spline method." International Journal of Computer Mathematics 87, no. 13 (2010): 3039–51. http://dx.doi.org/10.1080/00207160902878555.

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42

Wazwaz, Abdul-Majid, and Alice Gorguis. "An analytic study of Fisher's equation by using Adomian decomposition method." Applied Mathematics and Computation 154, no. 3 (2004): 609–20. http://dx.doi.org/10.1016/s0096-3003(03)00738-0.

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43

Frank, Steven A. "THE PRICE EQUATION, FISHER'S FUNDAMENTAL THEOREM, KIN SELECTION, AND CAUSAL ANALYSIS." Evolution 51, no. 6 (1997): 1712–29. http://dx.doi.org/10.1111/j.1558-5646.1997.tb05096.x.

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44

Tyson, John J., and Pavel K. Brazhnik. "On Traveling Wave Solutions of Fisher's Equation in Two Spatial Dimensions." SIAM Journal on Applied Mathematics 60, no. 2 (2000): 371–91. http://dx.doi.org/10.1137/s0036139997325497.

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45

Şahin, Ali, İdris Dağ, and Bülent Saka. "A B‐spline algorithm for the numerical solution of Fisher's equation." Kybernetes 37, no. 2 (2008): 326–42. http://dx.doi.org/10.1108/03684920810851212.

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46

FRIEDEN, B. ROY, and H. C. ROSU. "FISHER'S ARROW OF "TIME" IN COSMOLOGICAL COHERENT PHASE SPACE." Modern Physics Letters A 13, no. 01 (1998): 39–46. http://dx.doi.org/10.1142/s0217732398000073.

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Fisher's arrow of "time" in a cosmological phase space defined as in quantum optics (i.e. whose points are coherent states) is introduced as follows. Assuming that the phase space evolution of the universe states from an initial squeezed cosmological state towards a final thermal one, a Fokker–Planck equation for the time-dependent, cosmological Q phase space probability distribution can be written down. Next, using some recent results in the literature, we derive an information arrow of time for the Fisher phase space cosmological entropy based on the Q-function. We also mention the applicati

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47

SUCCI, SAURO. "A NOTE ON THE LATTICE BOLTZMANN VERSUS FINITE-DIFFERENCE METHODS FOR THE NUMERICAL SOLUTION OF THE FISHER'S EQUATION." International Journal of Modern Physics C 25, no. 01 (2013): 1340015. http://dx.doi.org/10.1142/s0129183113400159.

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We assess the Lattice Boltzmann (LB) method versus centered finite-difference schemes for the solution of the advection–diffusion–reaction (ADR) Fisher's equation. It is found that the LB method performs significantly better than centered finite-difference schemes, a property we attribute to the near absence of dispersion errors.

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48

Kaur, Jagbir, and Vivek Sangwan. "Stability estimates for singularly perturbed Fisher's equation using element-free Galerkin algorithm." AIMS Mathematics 7, no. 10 (2022): 19105–25. http://dx.doi.org/10.3934/math.20221049.

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<abstract><p>In the present article, a mesh-free technique has been presented to study the behavior of nonlinear singularly perturbed Fisher's problem, which exhibits the traveling wave propagation phenomenon. Some narrow regions adjacent to the left and right lateral boundary may possess rapid variations when the singular perturbation parameter $ \epsilon\rightarrow 0 $, which are not captured nicely by the traditional numerical schemes. In the current work, a robust numerical strategy is proposed, which comprises the implicit Crank-Nicolson scheme to discretize the time derivativ

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49

Wang, Tian-jun. "Generalized Laguerre spectral method for Fisher's equation on a semi-infinite interval." International Journal of Computer Mathematics 92, no. 5 (2014): 1039–52. http://dx.doi.org/10.1080/00207160.2014.920833.

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50

안영철 and Lee,Kab-Soo. "Application of Fisher's Equation on the Korea's Open Economy using System Dynamics." Journal of Asia-Pacific Studies 23, no. 1 (2016): 5–30. http://dx.doi.org/10.18107/japs.2016.23.1.001.

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