Problems of Optimization and Numerical Stability in Computations

Babuška, Ivo

doi:10.1007/978-3-642-11057-3_2

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Crank Nicolson Scheme1

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2017

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“…per Von-Neumann stability analysis). For this reason, whenever large time steps or high spatial resolution is necessary, the less accurate backward Euler method is often used, which is both stable and immune to oscillations [20]. In this method, consider the followings, …”

Section: Crank Nicolson Schemementioning

confidence: 99%

Numerical Study of One Dimensional Fishers KPP Equation with Finite Difference Schemes

Hasnain¹,

Saqib²

2017

AJCM

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In this paper, we originate results with finite difference schemes to approximate the solution of the classical Fisher Kolmogorov Petrovsky Piscounov (KPP) equation from population dynamics. Fisher's equation describes a balance between linear diffusion and nonlinear reaction. Numerical example illustrates the efficiency of the proposed schemes, also the Neumann stability analysis reveals that our schemes are indeed stable under certain choices of the model and numerical parameters. Numerical comparisons with analytical solution are also discussed. Numerical results show that Crank Nicolson and Richardson extrapolation are very efficient and reliably numerical schemes for solving one dimension fisher's KPP equation.

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Section: Crank Nicolson Schemementioning

confidence: 99%