$A preconditioned numerical solver for stiff nonlinear reaction–diffusion equations with fractional Laplacians that avoids dense matrices$

A preconditioned numerical solver for stiff nonlinear reaction–diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these opera...

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Veröffentlicht in:	Journal of computational physics 2015-04, Vol.287, p.254-268
Hauptverfasser:	Simmons, Alex, Yang, Qianqian, Moroney, Timothy
Format:	Artikel
Sprache:	eng
Schlagworte:	Backward differentiation formula Banded preconditioner Computation Computing time Contour integral method Differential equations Fractional Laplacian Jacobian-free Newton–Krylov Mathematical models Matrix representation Nonlinear Nonlinearity Operators Reaction-diffusion equations Solvers
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