Numerical approximation of inhomogeneous time fractional Burgers–Huxley equation with B-spline functions and Caputo derivative

A prototype model used to explain the relationship between mechanisms of reaction, convection effects, and transportation of diffusion is the generalized Burgers–Huxley equation. This study presents numerical solution of non-linear inhomogeneous time fractional Burgers–Huxley equation using cubic B-...

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Bibliographic Details
Published in:Engineering with computers 2022-06, Vol.38 (Suppl 2), p.885-900
Main Authors: Majeed, Abdul, Kamran, Mohsin, Asghar, Noreen, Baleanu, Dumitru
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Approximation
B spline functions
Basis functions
Boundary conditions
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Classical Mechanics
Collocation methods
Computer Science
Computer-Aided Engineering (CAD
Continuity (mathematics)
Control
Dependent variables
Diffusion effects
Investigations
Math. Applications in Chemistry
Mathematical and Computational Engineering
Norms
Original Article
Partial differential equations
Stability analysis
Systems Theory
Time dependence
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Summary:A prototype model used to explain the relationship between mechanisms of reaction, convection effects, and transportation of diffusion is the generalized Burgers–Huxley equation. This study presents numerical solution of non-linear inhomogeneous time fractional Burgers–Huxley equation using cubic B-spline collocation method. For this purpose, Caputo derivative is used for the temporal derivative which is discretized by L 1 formula and spatial derivative is interpolated with the help of B-spline basis functions, so the dependent variable is continuous throughout the solution range. The validity of the proposed scheme is examined by solving four test problems with different initial-boundary conditions. The algorithm for the execution of scheme is also presented. The effect of non-integer parameter α and time on dependent variable is studied. Moreover, convergence and stability of the proposed scheme is analyzed, and proved that scheme is unconditionally stable. The accuracy is checked by error norms. Based on obtained results we can say that the proposed scheme is a good addition to the existing schemes for such real-life problems.
ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-020-01261-y