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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.

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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