Abstract
In the present work, a high-order numerical scheme is proposed and analyzed to solve the non-linear time fractional reaction–diffusion equation (RDE) of order α∈(0,1). The numerical scheme consists of a time-stepping cubic approximation for the time fractional derivative and a compact finite difference scheme to approximate the spatial derivative. After applying these approximations to time fractional RDE, we get a non-linear system of equations. An iterative algorithm is formulated to solve the obtained nonlinear discrete system. We analyze the unique solvability of the proposed compact finite difference scheme and discuss the stability using von Neumann analysis. Further, we prove that the scheme is convergent in the Euclidean norm with the convergence order 4−α in the temporal direction and 4 in the spatial direction using matrix analysis. Finally, the numerical experimentation is performed to demonstrate the authenticity of the proposed numerical scheme.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
