Abstract
We consider the numerical solutions of the multi-term time fractional diffusion and diffusion-wave equations with variable coefficients in a bounded domain. The time fractional derivatives are described in the Caputo sense. A unified numerical scheme based on finite difference method in time and Legendre spectral method in space is proposed. Detailed error analysis is given for the fully discrete scheme. The convergence rate of the proposed scheme in L 2 norm is O ( τ 2 + N 1 − m ) , where τ , N , and m are the time-step size, polynomial degree, and regularity in the space variable of the exact solution, respectively. Numerical examples are presented to illustrate the theoretical results.
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.
