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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 \(\vartheta\)-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.

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35R10 Functional partial differential equations
35R11 Fractional partial differential equations
35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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