Solution of non-linear time fractional telegraph equation with source term using B-spline and Caputo derivative
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Abdul Majeed
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Mohsin Kamran
Abstract
This article focusses on the implementation of cubic B-spline approach to investigate numerical solutions of inhomogeneous time fractional nonlinear telegraph equation using Caputo derivative. L1 formula is used to discretize the Caputo derivative, while B-spline basis functions are used to interpolate the spatial derivative. For nonlinear part, the existing linearization formula is applied after generalizing it for all positive integers. The algorithm for the simulation is also presented. The efficiency of the proposed scheme is examined on three test problems with different initial boundary conditions. The influence of parameter α on the solution profile for different values is demonstrated graphically and numerically. Moreover, the convergence of the proposed scheme is analyzed and the scheme is proved to be unconditionally stable by von Neumann Fourier formula. To quantify the accuracy of the proposed scheme, error norms are computed and was found to be effective and efficient for nonlinear fractional partial differential equations (FPDEs).
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors have no conflict of interest.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Slippage phenomenon in hydromagnetic peristaltic rheology with hall current and viscous dissipation
- Dissipativity analysis of delayed stochastic generalized neural networks with Markovian jump parameters
- Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition
- The exact Riemann solutions to an isentropic non-ideal dusty gas flow under a magnetic field
- Higher order approximation of biharmonic problem using the WEB-Spline based mesh-free method
- Solution of non-linear time fractional telegraph equation with source term using B-spline and Caputo derivative
- Nonlinear stability and numerical simulations for a reaction–diffusion system modelling Allee effect on predators
- Computational analysis of heat and mass transfer in a micropolar fluid flow through a porous medium between permeable channel walls
- 3D structure of single and multiple vortices in a flow under rotation
- Interaction solutions of a variable-coefficient Kadomtsev–Petviashvili equation with self-consistent sources
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Slippage phenomenon in hydromagnetic peristaltic rheology with hall current and viscous dissipation
- Dissipativity analysis of delayed stochastic generalized neural networks with Markovian jump parameters
- Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition
- The exact Riemann solutions to an isentropic non-ideal dusty gas flow under a magnetic field
- Higher order approximation of biharmonic problem using the WEB-Spline based mesh-free method
- Solution of non-linear time fractional telegraph equation with source term using B-spline and Caputo derivative
- Nonlinear stability and numerical simulations for a reaction–diffusion system modelling Allee effect on predators
- Computational analysis of heat and mass transfer in a micropolar fluid flow through a porous medium between permeable channel walls
- 3D structure of single and multiple vortices in a flow under rotation
- Interaction solutions of a variable-coefficient Kadomtsev–Petviashvili equation with self-consistent sources
