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A high-order difference scheme for the generalized Cattaneo equation. (English) Zbl 1287.65068

Summary: A high-order finite difference scheme for the fractional Cattaneo equation is investigated. The \(L_1\) approximation is invoked for the time fractional part, and a compact difference scheme is applied to approximate the second-order space derivative. The stability and convergence rate are discussed in the maximum norm by the energy method. Numerical examples are provided to verify the effectiveness and accuracy of the proposed difference scheme.

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
35Q51 Soliton equations
35R11 Fractional partial differential equations
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