Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method

Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method

Abstract This article presents a numerical algorithm for solving time fractional Burgers’ and Fisher’s equations using cubic B-spline finite element method. The L1 formula with Caputo derivative is used to discretized the time fractional derivative, whereas the Crank–Nicolson scheme based on cubic B...

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Bibliographic Details
Main Authors: Abdul Majeed, Mohsin Kamran, Muhammad Kashif Iqbal, Dumitru Baleanu
Format: Article
Language:English
Published: SpringerOpen 2020-04-01
Series:Advances in Difference Equations
Subjects:
Cubic B-spline collocation method
Time fractional differential equation
Caputo’s fractional derivative
Stability and convergence
Finite difference formulation
Online Access:http://link.springer.com/article/10.1186/s13662-020-02619-8
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spelling doaj-7da8630ceb8247fda19f3a813267ba582020-11-25T03:49:29ZengSpringerOpenAdvances in Difference Equations1687-18472020-04-012020111510.1186/s13662-020-02619-8Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation methodAbdul Majeed0Mohsin Kamran1Muhammad Kashif Iqbal2Dumitru Baleanu3Department of Mathematics, Division of Science and Technology, University of EducationDepartment of Mathematics, Division of Science and Technology, University of EducationDepartment of Mathematics, Government College UniversityDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya UniversityAbstract This article presents a numerical algorithm for solving time fractional Burgers’ and Fisher’s equations using cubic B-spline finite element method. The L1 formula with Caputo derivative is used to discretized the time fractional derivative, whereas the Crank–Nicolson scheme based on cubic B-spline functions is used to interpolate the solution curve along the spatial grid. The numerical scheme has been implemented on three test problems. The obtained results indicate that the proposed method is a good option for solving nonlinear fractional Burgers’ and Fisher’s equations. The error norms L 2 $L_{2}$ and L ∞ $L_{\infty }$ have been calculated to validate the efficiency and accuracy of the presented algorithm.http://link.springer.com/article/10.1186/s13662-020-02619-8Cubic B-spline collocation methodTime fractional differential equationCaputo’s fractional derivativeStability and convergenceFinite difference formulation
collection DOAJ
language English
format Article
sources DOAJ
author Abdul Majeed
Mohsin Kamran
Muhammad Kashif Iqbal
Dumitru Baleanu
spellingShingle Abdul Majeed
Mohsin Kamran
Muhammad Kashif Iqbal
Dumitru Baleanu
Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method
Advances in Difference Equations
Cubic B-spline collocation method
Time fractional differential equation
Caputo’s fractional derivative
Stability and convergence
Finite difference formulation
author_facet Abdul Majeed
Mohsin Kamran
Muhammad Kashif Iqbal
Dumitru Baleanu
author_sort Abdul Majeed
title Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method
title_short Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method
title_full Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method
title_fullStr Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method
title_full_unstemmed Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method
title_sort solving time fractional burgers’ and fisher’s equations using cubic b-spline approximation method
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2020-04-01
description Abstract This article presents a numerical algorithm for solving time fractional Burgers’ and Fisher’s equations using cubic B-spline finite element method. The L1 formula with Caputo derivative is used to discretized the time fractional derivative, whereas the Crank–Nicolson scheme based on cubic B-spline functions is used to interpolate the solution curve along the spatial grid. The numerical scheme has been implemented on three test problems. The obtained results indicate that the proposed method is a good option for solving nonlinear fractional Burgers’ and Fisher’s equations. The error norms L 2 $L_{2}$ and L ∞ $L_{\infty }$ have been calculated to validate the efficiency and accuracy of the presented algorithm.
topic Cubic B-spline collocation method
Time fractional differential equation
Caputo’s fractional derivative
Stability and convergence
Finite difference formulation
url http://link.springer.com/article/10.1186/s13662-020-02619-8
work_keys_str_mv AT abdulmajeed solvingtimefractionalburgersandfishersequationsusingcubicbsplineapproximationmethod
AT mohsinkamran solvingtimefractionalburgersandfishersequationsusingcubicbsplineapproximationmethod
AT muhammadkashifiqbal solvingtimefractionalburgersandfishersequationsusingcubicbsplineapproximationmethod
AT dumitrubaleanu solvingtimefractionalburgersandfishersequationsusingcubicbsplineapproximationmethod
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