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A Petrov‐Galerkin method with quadrature for semi‐linear second‐order hyperbolic problems
Authors:B. Bialecki  M. Ganesh  K. Mustapha
Abstract:We propose and analyze a Crank–Nicolson quadrature Petrov–Galerkin (CNQPG) equation image ‐spline method for solving semi‐linear second‐order hyperbolic initial‐boundary value problems. We prove second‐order convergence in time and optimal order H2 norm convergence in space for the CNQPG scheme that requires only linear algebraic solvers. We demonstrate numerically optimal order Hk, k = 0,1,2, norm convergence of the scheme for some test problems with smooth and nonsmooth nonlinearities. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006
Keywords:hyperbolic initial–  boundary value problems  Petrov–  Galerkin  Crank‐Nicolson  splines  Gauss quadrature
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