A Novel Numerical Scheme for Time-Fractional Partial Integro Differential Equation of Parabolic Type - Kumar, Awinash; Gowrisankar, S. (Communications in Mathematics and Applications, 2024)
This work is devoted to study numerical methods for time-fractional integro-differential equations. In order to compute the approximate solutions for highly non-linear or linear forms of various time-fractional integro-differential models, we apply the extended and more generalized finite difference methods. First order and second order spacial derivatives are approximated by the central difference. The integral terms and Capto fractional terms are approximated by the composite trapezoidal rule. Particularly we derive error estimation and stability analysis of the finite difference method for a Volterra type fractional differential equation. Illustrative examples are provided in support of the proposed methods with three distinct problems.
Keywords: Time-fractional ADE; Variable parameters; Finite difference methods; Convergence analysis; Integro-partial differential equations