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2006•Mathematical Problems in EngineeringOpen access

Homotopy perturbation method for the solution of the electrostatic potential differential equation

Lina Zhang, Ji‐Huan He

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Abstract

This paper obtains an explicit analytical solution for nonlinear Poisson‐Boltzmann equation by the homotopy perturbation method, which does not require a small parameter in the equation under study, so it can be applied to both the weakly and strongly nonlinear problems. The obtained results show the evidence of the usefulness of the homotopy perturbation method for obtaining approximate analytical solutions for nonlinear equations.

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What this paper is about

This paper obtains an explicit analytical solution for nonlinear Poisson‐Boltzmann equation by the homotopy perturbation method, which does not require a small parameter in the equation under study, so it can be applied to both the weakly and strongly nonlinear problems. The obtained results show the evidence of the usefulness of the homotopy perturbation method for obtaining approximate analytical solutions for nonlinear equations.

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OpenAlex reports 36 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper obtains an explicit analytical solution for nonlinear Poisson‐Boltzmann equation by the homotopy perturbation method, which does not require a small parameter in the equation under study, so it can be applied to both the weakly and strongly nonlinear problems. The obtained results show the evidence of the usefulness of the homotopy perturbation method for obtaining approximate analytical solutions for nonlinear equations.

Key concepts: Homotopy perturbation method, Homotopy analysis method, Perturbation (astronomy), Mathematical analysis, Mathematics, Differential equation, Applied mathematics, Physics

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