Convergence analysis and approximation solution for the coupled fractional convection-diffusion equations


Authors

Davood Rostamy - Department of Mathematics, Imam Khomeini International University, Qazvin, I. R. Iran. Ehsan Mottaghi - Department of Mathematics, Imam Khomeini International University, Qazvin, I. R. Iran.


Abstract

By using maximum principle approach, the existence, uniqueness and stability of a coupled fractional partial differential equations is studied. A new fractional characteristic finite difference scheme is given for solving the coupled system. This method is based on shifted Grünwald approximation and Diethelm's algorithm. We obtain the optimal convergence rate for this scheme and drive the stability estimates. The results are justified by implementing an example of the fractional order time and space dependent in concept of the complex Lévy motion. Also, the numerical results are examined for disinfection and sterilization of tetanus.


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