Numerical investigation of spatial-temporal model of microorganism populations with nonlocal interaction

Timofeeva, Tatiyana S.; Vinokurova, Sakhayana S.

doi:10.1063/5.0107070

Cited by 1 publication

(1 citation statement)

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“…A mixed modal discontinuous Galerkin scheme for solving the Fisher–KPP equation is applied by Singh and Satyvir [18]. A linearized implicit finite difference scheme approximating the generalized Fisher–KPP model is constructed and implemented by Timofeeva et al [19]. Billingham and Needham [20] discuss nonnegative traveling wave solutions the cubic nonlocal Fisher–KPP equation in one spatial dimension.…”

Section: Introductionmentioning

confidence: 99%

A mathematical modeling and numerical study for stochastic Fisher–SI model driven by space uniform white noise

Uma

Jafari

Balachandar

et al. 2023

Math Methods in App Sciences

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In this study, we propose an approximate solution based on two‐dimensional shifted Legendre polynomials to solve nonlinear stochastic partial differential equations with variable coefficients. For this purpose, we have considered a Fisher‐Kolmogorov‐Petrovsky‐Piskunov (Fisher–KPP) equation with space uniform white noise for the same. New stochastic operational matrix of integration based on shifted Legendre polynomials is generated. This operational matrix reduces the problem under study into solving a system of algebraic equations. The convergence analysis is discussed, and the error bound in L2$$ {L}^2 $$ norm is derived and obtained as ‖‖eNfalse(t,xfalse)2≤6Kfalse(16N4false)2false(1−6Sfalse)$$ {\left\Vert {e}_N\left(t,x\right)\right\Vert}^2\le \frac{6K}{{\left(16{N}^4\right)}^2\left(1-6S\right)} $$. The theoretical analysis confirms that as the degree of the approximation polynomial is increased, the solution is on par with the exact solution. The numerical examples confirm the accuracy and the applicability of the proposed method. A comparative study is carried out with explicit 1.5 order Runge–Kutta method. The time complexity of the proposed technique is also studied.

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Section: Introductionmentioning

confidence: 99%