Enhancing the accuracy and efficiency of two uniformly convergent numerical solvers for singularly perturbed parabolic convection–diffusion–reaction problems with two small parameters

• Autorzy: Ansari Khursheed J. , Izadi Mohammad , Noeiaghdam Samad

Identyfikatory

DOI

10.1515/dema-2023-0144

• Języki publikacji: EN

Abstrakty

EN

This study is devoted to designing two hybrid computational algorithms to find approximate solutions for a class of singularly perturbed parabolic convection–diffusion–reaction problems with two small parameters. In our approaches, the time discretization is first performed by the well-known Rothe method and Taylor series procedures, which reduce the underlying model problem into a sequence of boundary value problems (BVPs). Hence, a matrix collocation technique based on novel shifted Delannoy functions (SDFs) is employed to solve each BVP at each time step. We show that our proposed hybrid approximate techniques are uniformly convergent in order [formula], where Δτ is the time step and M is the number of SDFs used in the approximation. Numerical simulations are performed to clarify the good alignment between numerical and theoretical findings. The computational results are more accurate as compared with those of existing numerical values in the literature.

Słowa kluczowe

EN

collocation point; convergent analysis; Delannoy functions; stability; Taylor expansion; Rothe method; singularly perturbed problem

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20230144
• Opis fizyczny: Bibliogr. 42 poz., rys., tab.

Twórcy

autor

Ansari Khursheed J.

• Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia

autor

Izadi Mohammad

• Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

autor

Noeiaghdam Samad

• Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk, 664074, Russia
• Department of Applied Mathematics and Programming, South Ural State University, Lenin prospect 76, Chelyabinsk, 454080, Russia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).