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Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations. (English) Zbl 1093.65096
The authors propose a numerical method for a parabolic equation with delay. The spatial derivative is handled with spectral collocation, and the resulting system of ordinary differential equations is solved by waveform relaxation, which is a form of Picard iteration. It is shown that the method converges.

MSC:
65M70 Spectral, collocation and related 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
35R10 Functional partial differential equations
35K55 Nonlinear parabolic equations
Software:
Matlab
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References:
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