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Abstract
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The aim of this work is to propose a numerical approach based on the local weak formulations and
finite difference scheme to solve the two-dimensional fractional-time convection–diffusion–reaction
equations. The numerical studies on sensitivity analysis to parameter and convergence analysis show
that our approach is stable. Moreover, numerical demonstrations are given to show that the weak-form
approach is applicable to a wide range of problems; in particular, a forced-subdiffusion–convection
equation previously solved by a strong-form approach with weak convection is considered. It is shown
that our approach can obtain comparable simulations not only in weak convection but also in
convection dominant cases. The simulations to a subdiffusion–convection–reaction equation are also
presented.
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