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The formally second-order BDF ADI difference/compact difference scheme for the nonlocal evolution problem in three-dimensional space. (English) Zbl 07441561

Summary: This work formulates two kinds of alternating direction implicit (ADI) schemes for the parabolic-type three-dimensional evolution equation with a weakly singular kernel. The second-order backward differentiation formula (BDF2) and the second-order convolution quadrature (CQ) technique are applied to the discretization of the time derivative and the Riemann-Liouville (R-L) integral, respectively. Then, the fully-discrete BDF2 difference scheme and BDF2 compact difference scheme are constructed via the general centered difference and compact difference method, respectively. Meanwhile, the ADI algorithms are designed reasonably for two schemes to reduce the computational cost. The stability and convergence of two ADI schemes are derived via the energy method. Finally, several numerical examples are provided and tested to validate the theoretical analysis.

MSC:

65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
35R11 Fractional partial differential equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Software:

Algorithm 986
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References:

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