Numerical Solution of the Equation with an Angular Boundary Layer
<p id="p2">This work is devoted to a numerical method for solving a first-order partial differential equation when a small parameter is present in all derivatives. A numerical method based on a synthesis of S.A. The Lomov method and the finite-difference method are proposed. In the second part, a re...
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| Autores principales: | , , |
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| Formato: | Capítulo de libro |
| Lenguaje: | inglés |
| Publicado: |
IntechOpen
2025
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| Materias: | |
| Acceso en línea: | https://www.intechopen.com/chapters/1206752 |
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| Sumario: | <p id="p2">This work is devoted to a numerical method for solving a first-order partial differential equation when a small parameter is present in all derivatives. A numerical method based on a synthesis of S.A. The Lomov method and the finite-difference method are proposed. In the second part, a regularized asymptotic of any order of a mixed problem is constructed for a first-order partial differential equation, when the limit equation has a regular singularity. The constructed asymptotic contains boundary layer functions of three types: power, exponential, and angular functions. The asymptotic of the solution is constructed by a special class of functions corresponding to the structure of the fundamental system of solutions. The solution to the problem is sought in the form of a polynomial in powers of a small parameter. The asymptotic character of the constructed solution is established.</p> |
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| ISBN: | 978-0-85014-981-4 |
| DOI: | 10.5772/intechopen.1009454 |