Epidemic processes with vaccination and immunity loss studied with the BLUES function method

Berx, Jonas; Indekeu, Joseph

doi:10.1016/j.physa.2021.126724

Cited by 3 publications

(3 citation statements)

References 12 publications

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“…For nonlinear ODEs with source or sink terms, the BLUES function method has been studied intensively [7,8,9,11] and anticipated in [12]. For PDEs with a first-order time derivative, the role of the source was taken up by the initial condition multiplied by a Dirac point source located at t = 0 [10].…”

Section: Blues Function Methods For Nth-order Time Derivativesmentioning

confidence: 99%

“…Consequently, we probed the usefulness of the BLUES function method in the arena of nonlinear partial differential equations (PDEs) with a first-order time derivative where the initial condition plays the role of the inhomogeneous source by multiplication with a Dirac delta point source located at time t = 0 [10]. It was shown that the method produces globally convergent approximants with high accuracy for systems of coupled nonlinear first-order ODEs when the fixed points of the system are introduced into the linear operator [11]. However, for second-order time derivatives, the BLUES function method needs to be modified.…”

Section: Introductionmentioning

confidence: 99%

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The BLUES function method for second-order partial differential equations: application to a nonlinear telegrapher equation

Berx,

Indekeu

2022

Preprint

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An analytic iteration sequence based on the extension of the BLUES (Beyond Linear Use of Equation Superposition) function method to partial differential equations (PDEs) with secondorder time derivatives is studied. The original formulation of the BLUES method is modified by introducing a matrix formalism that takes into account the initial conditions for higher-order time derivatives. The initial conditions of both the solution and its derivatives now play the role of a source vector. The method is tested on a nonlinear telegrapher equation, which can be reduced to a nonlinear wave equation by a suitable choice of parameters. In addition, a comparison is made with three other methods: the Adomian decomposition method, the variational iteration method (with Green function) and the homotopy perturbation method. The matrix BLUES function method is shown to be a worthwhile alternative for the other methods.

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Section: Blues Function Methods For Nth-order Time Derivativesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The BLUES function method for second-order partial differential equations: application to a nonlinear telegrapher equation

Berx,

Indekeu

2022

Preprint

Self Cite

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“…Therefore, it is appropriate to look for approximate solutions instead of trying to solve the differential equations directly. To this end, (semi-)analytical iterative methods such as the variational iteration method (VIM) [1,2,3], Adomian decomposition method (ADM) [4,5], homotopy perturbation method (HPM) [6] or BLUES function method [7,8,9,10] have been proposed.…”

Section: Introductionmentioning

confidence: 99%

Convergence acceleration for the BLUES function method

Berx¹

2022

Preprint

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A detailed comparison is made between four different iterative procedures: Picard, Ishikawa, Mann and Picard-Krasnoselskii, within the framework of the BLUES function method and the variational iteration method. The resulting modified methods are subsequently applied to a nonlinear reaction-diffusion-advection differential equation to generate approximations to the known exact solution. The differences between the BLUES function method and the variational iteration method are illustrated by studying the approximants and the error between the obtained approximants and the exact solution.

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The BLUES function method for second-order partial differential equations: Application to a nonlinear telegrapher equation

Berx

Indekeu

2022

Partial Differential Equations in Applied Mathematics

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Epidemic processes with vaccination and immunity loss studied with the BLUES function method

Cited by 3 publications

References 12 publications

The BLUES function method for second-order partial differential equations: application to a nonlinear telegrapher equation

The BLUES function method for second-order partial differential equations: application to a nonlinear telegrapher equation

Convergence acceleration for the BLUES function method

The BLUES function method for second-order partial differential equations: Application to a nonlinear telegrapher equation

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