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- Title
Approximate Analytical Solutions for Strongly Coupled Systems of Singularly Perturbed Convection–Diffusion Problems.
- Authors
El-Zahar, Essam R.; Al-Boqami, Ghaliah F.; Al-Juaydi, Haifa S.
- Abstract
This work presents a reliable algorithm to obtain approximate analytical solutions for a strongly coupled system of singularly perturbed convection–diffusion problems, which exhibit a boundary layer at one end. The proposed method involves constructing a zero-order asymptotic approximate solution for the original system. This approximation results in the formation of two systems: a boundary layer system with a known analytical solution and a reduced terminal value system, which is solved analytically using an improved residual power series approach. This approach combines the residual power series method with Padé approximation and Laplace transformation, resulting in an approximate analytical solution with higher accuracy compared to the conventional residual power series method. In addition, error estimates are extracted, and illustrative examples are provided to demonstrate the accuracy and effectiveness of the method.
- Subjects
ANALYTICAL solutions; SINGULAR perturbations; LAPLACE transformation; POWER series; BOUNDARY layer (Aerodynamics); PADE approximant
- Publication
Mathematics (2227-7390), 2024, Vol 12, Issue 2, p277
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math12020277