A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic Bspline functions
Abstract We present a collocation approach based on redefined cubic Bspline (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 α ∈ ( 0 , 1 ] $\alpha\in(0,1]$ by usin...
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20200401

Series:  Advances in Difference Equations 
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Online Access:  http://link.springer.com/article/10.1186/s1366202002616x 
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doaj7aa592b0f3f14481b9bb07f5b332320020201125T03:10:23ZengSpringerOpenAdvances in Difference Equations16871847202004012020112210.1186/s1366202002616xA numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic Bspline functionsNauman Khalid0Muhammad Abbas1Muhammad Kashif Iqbal2Dumitru Baleanu3Department of Mathematics, National College of Business Administration & EconomicsInformetrics Research Group, Ton Duc Thang UniversityDepartment of Mathematics, Government College UniversityDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya UniversityAbstract We present a collocation approach based on redefined cubic Bspline (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 α ∈ ( 0 , 1 ] $\alpha\in(0,1]$ 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 ( h 2 + Δ t 2 − α ) $O(h^{2}+\Delta t^{2\alpha})$ 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.http://link.springer.com/article/10.1186/s1366202002616xRedefined cubic Bspline functionsTime fractional Allen–Cahn equationCaputo’s time fractional derivativeStability and convergenceFinite difference formulation 
collection 
DOAJ 
language 
English 
format 
Article 
sources 
DOAJ 
author 
Nauman Khalid Muhammad Abbas Muhammad Kashif Iqbal Dumitru Baleanu 
spellingShingle 
Nauman Khalid Muhammad Abbas Muhammad Kashif Iqbal Dumitru Baleanu A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic Bspline functions Advances in Difference Equations Redefined cubic Bspline functions Time fractional Allen–Cahn equation Caputo’s time fractional derivative Stability and convergence Finite difference formulation 
author_facet 
Nauman Khalid Muhammad Abbas Muhammad Kashif Iqbal Dumitru Baleanu 
author_sort 
Nauman Khalid 
title 
A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic Bspline functions 
title_short 
A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic Bspline functions 
title_full 
A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic Bspline functions 
title_fullStr 
A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic Bspline functions 
title_full_unstemmed 
A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic Bspline functions 
title_sort 
numerical investigation of caputo time fractional allen–cahn equation using redefined cubic bspline functions 
publisher 
SpringerOpen 
series 
Advances in Difference Equations 
issn 
16871847 
publishDate 
20200401 
description 
Abstract We present a collocation approach based on redefined cubic Bspline (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 α ∈ ( 0 , 1 ] $\alpha\in(0,1]$ 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 ( h 2 + Δ t 2 − α ) $O(h^{2}+\Delta t^{2\alpha})$ 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. 
topic 
Redefined cubic Bspline functions Time fractional Allen–Cahn equation Caputo’s time fractional derivative Stability and convergence Finite difference formulation 
url 
http://link.springer.com/article/10.1186/s1366202002616x 
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