Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problems

• Published in: Mathematical modelling and analysis Vol. 26; no. 1; pp. 116 - 134
• Main Authors: Abbasbandy, Saeid, Sahihi, Hussein, Allahviranloo, Tofigh
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 01.01.2021
• Subjects: Analysis; Boundary layer; boundary layer behavior; Boundary layers; Convection; error analysis; Kernels; Methods; reproducing kernel method; singularly perturbed parabolic problems; boundary layer behavior; singularly perturbed parabolic problems; error analysis; reproducing kernel method
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2021.12057

In the present paper, reproducing kernel method (RKM) is introduced, which is employed to solve singularly perturbed convection-diffusion parabolic problems (SPCDPPs). It is noteworthy to mention that regarding very serve singularities, there are regular boundary layers in SPCDPPs. On the other hand, getting a reliable approximate solution could be difficult due to the layer behavior of SPCDPPs. The strategy developed in our method is dividing the problem region into two regions, so that one of them would contain a boundary layer behavior. For more illustrations of the method, certain linear and nonlinear SPCDPP are solved.