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Nonlinear stability and convergence of finite-difference methods for the ”good” Boussinesq equation. (English) Zbl 0749.65082
Summary: The “good” Boussinesq equation \(u_{tt}=-u_{xxxx}+u_{xx}+(u^ 2)_{xx}\) has recently been found to possess an interesting soliton- interaction mechanism. In this paper we study the nonlinear stability and the convergence of some simple finite-difference schemes for the numerical solution of problems involving the “good” Boussinesq equation. Numerical experiments are also reported.

65Z05 Applications to the sciences
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
35L75 Higher-order nonlinear hyperbolic equations
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