Numerical solutions of random mean square Fisher‐KPP models with advection

Casabán, M.-C.; Jódar, L.

doi:10.1002/mma.5942

Cited by 3 publications

(3 citation statements)

References 29 publications

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“…where Ė is the shifted Legendre coefficient approximation of the unit step function and 29) in (24),…”

Section: Proposed Methodologymentioning

confidence: 99%

“…A positivity and boundedness preserving difference scheme is studied by Dingwen and Zilin [23]. In their article, Casabán et al [24] discuss the numerical solutions of random mean square Fisher–KPP models with advection. In their article, Blath et al [25] discuss the existence and uniqueness of a class of SPDEs with seed bank, modeling the spread of a beneficial allele in a spatial population.…”

Section: Introductionmentioning

confidence: 99%

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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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“…where Ė is the shifted Legendre coefficient approximation of the unit step function and 29) in (24),…”

Section: Proposed Methodologymentioning

confidence: 99%

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

View full text Add to dashboard Cite

show abstract

“…Another powerful technique suitable for models with complex geometries is the finite element method [9]. Iterative methods, for instance FD have particular troubles derived from the storage accumulation of intermediate levels when the computer manages symbolically the involved stochastic processes, [10][11][12]. This drawback of the iterative methods for solving PDEM occurs in both approaches, the one based on Itô calculus [13] the so-called stochastic differential approach (SDEA), as well as the one based on the mean square calculus [14] also called random differential equations approach (RDEA).…”

Section: Introductionmentioning

confidence: 99%

Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness

2021

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This paper deals with the search for reliable efficient finite difference methods for the numerical solution of random heterogeneous diffusion reaction models with a finite degree of randomness. Efficiency appeals to the computational challenge in the random framework that requires not only the approximating stochastic process solution but also its expectation and variance. After studying positivity and conditional random mean square stability, the computation of the expectation and variance of the approximating stochastic process is not performed directly but through using a set of sampling finite difference schemes coming out by taking realizations of the random scheme and using Monte Carlo technique. Thus, the storage accumulation of symbolic expressions collapsing the approach is avoided keeping reliability. Results are simulated and a procedure for the numerical computation is given.

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Integral transform solution of random coupled parabolic partial differential models

Casabán

Egorova

Jódar

2020

Math Methods in App Sciences

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This paper deals with the construction of random power series solution of second order linear differential equations of Hermite containing uncertainty through its coefficients and initial conditions. Under appropriate hypotheses on the data, we establish that the constructed random power series solution is mean square convergent. We provide conditions in order to obtain random polynomial solutions and, as a consequence, random Hermite polynomial are introduced. Also, the main statistical functions of the approximate stochastic process solution generated by truncation of the exact power series solution are given. Finally, we apply the proposed technique to several illustrative examples comparing the numerical results with respect to those provided by other available approaches including Monte Carlo simulation.

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Numerical solutions of random mean square Fisher‐KPP models with advection

Cited by 3 publications

References 29 publications

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

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

Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness

Integral transform solution of random coupled parabolic partial differential models

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