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Collocation solution for RLW equation with septic spline. (English) Zbl 1061.65102
Summary: A collocation solution using the septic splines as a shape function for the regularized long wave (RLW) equation is presented. A linear stability analysis shows the scheme to be unconditionally stable. Test problems which, migration and interaction of solitary waves, are used to validate our scheme by calculate \(L_2\)-norm and \(L_{\infty}\)-norm, and three invariants of motion are evaluates to determine the conservation properties of the algorithm. The numerical scheme is compared with other published methods and shown to be accurate and efficient

65M70 Spectral, collocation and related 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
35L75 Higher-order nonlinear hyperbolic equations
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