ADI Compact Difference Scheme for the Two-Dimensional Integro-Differential Equation with Two Fractional Riemann–Liouville Integral Kernels
Ziyi Chen, Haixiang Zhang, Hu Chen
Abstract
In this paper, a numerical method of a two-dimensional (2D) integro-differential equation with two fractional Riemann–Liouville (R-L) integral kernels is investigated. The compact difference method is employed in the spatial direction. The integral terms are approximated by a second-order convolution quadrature formula. The alternating direction implicit (ADI) compact difference scheme reduces the CPU time for two-dimensional problems. Simultaneously, the stability and convergence of the proposed ADI compact difference scheme are demonstrated. Finally, two numerical examples are provided to verify the established ADI compact difference scheme.
Topics & Concepts
MathematicsIntegro-differential equationScheme (mathematics)Mathematical analysisFractional calculusDifferential equationFirst-order partial differential equationFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsNumerical methods for differential equations