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A linearized compact difference scheme for a class of nonlinear delay partial differential equations. (English) Zbl 1352.65270
Summary: A linearized compact difference scheme is presented for a class of nonlinear delay partial differential equations with initial and Dirichlet boundary conditions. The unique solvability, unconditional convergence and stability of the scheme are proved. The convergence order is $$O(\tau^2+h^4)$$ in $$L_\infty$$ norm. Finally, a numerical example is given 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
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