A Numerical Investigation of Caputo Time Fractional Allen-Cahn Equation Using Redefined Cubic B-Spline Functions
| dc.contributor.author | Abbas, Muhammad | |
| dc.contributor.author | Iqbal, Muhammad Kashif | |
| dc.contributor.author | Baleanu, Dumitru | |
| dc.contributor.author | Khalid, Nauman | |
| dc.date.accessioned | 2021-01-28T12:21:12Z | |
| dc.date.accessioned | 2025-09-18T16:08:31Z | |
| dc.date.available | 2021-01-28T12:21:12Z | |
| dc.date.available | 2025-09-18T16:08:31Z | |
| dc.date.issued | 2020 | |
| dc.description | Abbas, Dr. Muhammad/0000-0002-0491-1528; Iqbal, Muhammad Kashif/0000-0003-4442-7498 | en_US |
| dc.description.abstract | We present a collocation approach based on redefined cubic B-spline (RCBS) functions and finite difference formulation to study the approximate solution of time fractional Allen-Cahn equation (ACE). We discretize the time fractional derivative of order alpha is an element of (0,1] by using finite forward difference formula and bring RCBS functions into action for spatial discretization. We find that the numerical scheme is of order O(h2+Delta t2-alpha) and unconditionally stable. We test the computational efficiency of the proposed method through some numerical examples subject to homogeneous/nonhomogeneous boundary constraints. The simulation results show a superior agreement with the exact solution as compared to those found in the literature. | en_US |
| dc.identifier.citation | Khalid, Nauman...et al. (2020). "A numerical investigation of Caputo time fractional Allen-Cahn equation using redefined cubic B-spline functions", Advances in Difference Equations, Vol. 2020, No. 1. | en_US |
| dc.identifier.doi | 10.1186/s13662-020-02616-x | |
| dc.identifier.issn | 1687-1847 | |
| dc.identifier.scopus | 2-s2.0-85083512717 | |
| dc.identifier.uri | https://doi.org/10.1186/s13662-020-02616-x | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12416/15064 | |
| dc.language.iso | en | en_US |
| dc.publisher | Springer | en_US |
| dc.relation.ispartof | Advances in Difference Equations | |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Redefined Cubic B-Spline Functions | en_US |
| dc.subject | Time Fractional Allen-Cahn Equation | en_US |
| dc.subject | Caputo'S Time Fractional Derivative | en_US |
| dc.subject | Stability And Convergence | en_US |
| dc.subject | Finite Difference Formulation | en_US |
| dc.title | A Numerical Investigation of Caputo Time Fractional Allen-Cahn Equation Using Redefined Cubic B-Spline Functions | en_US |
| dc.title | A numerical investigation of Caputo time fractional Allen-Cahn equation using redefined cubic B-spline functions | tr_TR |
| dc.type | Article | en_US |
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| gdc.author.id | Abbas, Dr. Muhammad/0000-0002-0491-1528 | |
| gdc.author.id | Iqbal, Muhammad Kashif/0000-0003-4442-7498 | |
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| gdc.author.wosid | Abbas, Muhammad/K-8190-2019 | |
| gdc.author.wosid | Baleanu, Dumitru/B-9936-2012 | |
| gdc.author.wosid | Iqbal, Muhammad Kashif/Hkm-9371-2023 | |
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| gdc.description.department | Çankaya University | en_US |
| gdc.description.departmenttemp | [Khalid, Nauman] Natl Coll Business Adm & Econ, Dept Math, Lahore, Pakistan; [Abbas, Muhammad] Ton Duc Thang Univ, Informetr Res Grp, Ho Chi Minh City, Vietnam; [Abbas, Muhammad] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam; [Abbas, Muhammad] Univ Sargodha, Dept Math, Sargodha, Pakistan; [Iqbal, Muhammad Kashif] Govt Coll Univ, Dept Math, Faisalabad, Pakistan; [Baleanu, Dumitru] Cankaya Univ, Fac Arts & Sci, Dept Math, Ankara, Turkey; [Baleanu, Dumitru] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan; [Baleanu, Dumitru] Inst Space Sci, Magurele, Romania | en_US |
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| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| gdc.description.volume | 2020 | en_US |
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| gdc.oaire.keywords | Stability and convergence | |
| gdc.oaire.keywords | Numerical Analysis | |
| gdc.oaire.keywords | Time-Fractional Diffusion Equation | |
| gdc.oaire.keywords | Statistical and Nonlinear Physics | |
| gdc.oaire.keywords | Time fractional Allen–Cahn equation | |
| gdc.oaire.keywords | Computer science | |
| gdc.oaire.keywords | Finite difference formulation | |
| gdc.oaire.keywords | Algorithm | |
| gdc.oaire.keywords | Fractional Derivatives | |
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| gdc.oaire.keywords | Numerical Methods for Singularly Perturbed Problems | |
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| gdc.oaire.keywords | QA1-939 | |
| gdc.oaire.keywords | FOS: Mathematics | |
| gdc.oaire.keywords | Redefined cubic B-spline functions | |
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| gdc.oaire.keywords | Anomalous Diffusion Modeling and Analysis | |
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| gdc.oaire.keywords | Caputo’s time fractional derivative | |
| gdc.oaire.keywords | Rogue Waves in Nonlinear Systems | |
| gdc.oaire.keywords | redefined cubic B-spline functions | |
| gdc.oaire.keywords | Fractional derivatives and integrals | |
| gdc.oaire.keywords | Fractional partial differential equations | |
| gdc.oaire.keywords | finite difference formulation | |
| gdc.oaire.keywords | time fractional Allen-Cahn equation | |
| gdc.oaire.keywords | stability and convergence | |
| gdc.oaire.keywords | Caputo's time fractional derivative | |
| gdc.oaire.keywords | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs | |
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