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Numerical Resolution of Differential Equations Using the Finite Difference Method in the Real and Complex Domain

Ana Laura Mendonça Almeida Magalhães, Pedro Paiva Brito

2024Englishfinite differencedifferential equationscomplex variablesnumerical methodserror analysiselasticity

Abstract

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The paper expands the finite difference method to the complex plane, and thus obtains an improvement in the resolution of differential equations with an increase in numerical precision and a generalization in the mathematical modeling of problems. The article begins with a selection of the best techniques for obtaining finite difference coefficients for approximating derivatives in the real domain. Then, the calculation is expanded to the complex domain. The research expands forward, backward, and central difference approximations of the real case by a quadrant approximation in the complex plane, which facilitates the use in boundary conditions of differential equations. The article shows many real and complex finite difference equations with their respective order of error.

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Cite This Work

@article{61ebc99f-4a16-49ec-ba01-a5406c3fb331,
  title={Numerical Resolution of Differential Equations Using the Finite Difference Method in the Real and Complex Domain},
  author={Ana Laura Mendonça Almeida Magalhães and Pedro Paiva Brito},
  year={2024},
  language={English}
}
TY  - JOUR
TI  - Numerical Resolution of Differential Equations Using the Finite Difference Method in the Real and Complex Domain
AU  - Ana Laura Mendonça Almeida Magalhães
AU  - Pedro Paiva Brito
PY  - 2024
LA  - English
ER  -

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