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This research aims to find numerical solutions for the one-dimensional Poisson problem using iterative methods and sparse matrices.

April 10, 2026Open Access

Numerical Solution of the One-Dimensional Poisson Problem via Iterative Methods and Sparse Matrices

Key Points

This research aims to find numerical solutions for the one-dimensional Poisson problem using iterative methods and sparse matrices.
Applied finite difference discretization to formulate linear systems.
Evaluated Gauss-Seidel and Successive Over-Relaxation (SOR) methods.
Conducted numerical experiments to analyze convergence and efficiency.
Both Gauss-Seidel and SOR methods demonstrated effective convergence.
Sparse matrix structures enhanced the efficiency of the computations.
Numerical experiments confirmed the suitability of iterative methods for this problem.

Abstract

We present the numerical solution of the one-dimensional Poisson problem using sparse matrix structures and iterative methods. We analyze the performance of the Gauss–Seidel and Successive Over-Relaxation (SOR) methods applied to the resulting linear systems obtained via finite difference discretization. Numerical experiments illustrate the convergence behavior and efficiency of these methods.

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Authors

Lorena Vitoria da Silva

Alvaro Julio Yucra Hancco

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Institutions

Universidade Federal do Tocantins

Universidade Federal do Norte do Tocantins

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Numerical Solution of the One-Dimensional Poisson Problem via Iterative Methods and Sparse Matrices

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Abstract

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Discussion

Authors

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References and Citations

Citation Network

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