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Computational methods for delay parabolic and time-fractional partial differential equations. (English) Zbl 1204.65114
Summary: This article is concerned with ϑ-methods for delay parabolic partial differential equations. The methodology is extended to time-fractional-order parabolic partial differential equations in the sense of Caputo. The fully implicit scheme preserves delay-independent asymptotic stability and the solution continuously depends on the time-fractional order. Several numerical examples of interest are included to demonstrate the effectiveness of the method.
MSC:
65M20Method of lines (IVP of PDE)
35R10Partial functional-differential equations
35R11Fractional partial differential equations
35K61Nonlinear parabolic equations, nonlinear initial boundary value problems
65M12Stability and convergence of numerical methods (IVP of PDE)
65M06Finite difference methods (IVP of PDE)