Advanced International Journal for Research

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Volume 7 Issue 3
May-June 2026

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Electrostatic Potential Modeling Using Numerical Methods: Analysis of ADI and Standard Five-Point Schemes

Author(s) Prof. Dr. Malabika Adak
Country India
Abstract Accurate evaluation of electrostatic potential distribution is essential in diverse fields such as semiconductor device modeling, electromagnetic field analysis, and steady-state heat transfer. This work presents a comparative study of two numerical approaches—the Alternating Direction Implicit (ADI) method and the Standard Five-Point (SFP) finite difference scheme—for solving the two-dimensional Laplace equation on square and rectangular domains with Dirichlet boundary conditions. The ADI method, known for its unconditional stability and efficiency, is implemented in MATLAB and applied to large grid systems, while the SFP scheme provides a direct and straightforward discretization framework. Numerical solutions are validated against analytical results obtained using the separation of variables method. The comparative analysis emphasizes accuracy, convergence characteristics, and computational efficiency. Results indicate that while the SFP method performs reliably for smaller grids, the ADI approach demonstrates faster convergence and superior performance for larger domains. These findings highlight the strengths and limitations of both methods and offer guidance for selecting appropriate numerical techniques in electrostatic potential modeling.
Keywords Electrostatic potential distribution, Alternating Direction Implicit method, Standard Five-Point scheme, Dirichlet boundary condition, Laplace equation.
Field Engineering
Published In Volume 7, Issue 3, May-June 2026
Published On 2026-06-11
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E-ISSN 3048-7641
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