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A Crank-Nicolson scheme for a class of delay nonlinear parabolic differential equations. (Chinese. English summary) Zbl 1240.65266

Summary: A linearized Crank-Nicolson scheme is established for a class of delay nonlinear parabolic differential equations with Dirichlet boundary value conditions. It is proved that the difference scheme is unconditionally stable and convergent in the \(L_\infty\)-norm. The convergence order is \(O(r^2 + h^2)\). Finally, a numerical example is provided to support the theoretical results.

MSC:

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
35R10 Partial functional-differential equations
35K55 Nonlinear parabolic equations
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