A qualocation method for parabolic partial differential equations
Copyright policy )A qualocation method for parabolic partial differential equations
For a semilinear parabolic partial differential equation in one space dimension, the numerical approximation by means of a qualocation method (a quadrature-based modification of a collocation method) is studied. After a Galerkin ansatz with piecewise cubic polynomials, the appearing integrals are approximated using a fourth-order composite two-point Gauss quadrature. The author proves a priori error estimates and superconvergence results for smooth solutions. Furthermore, the time discretization via linearized implicit Euler and extrapolated Crank-Nicolson scheme is analyzed.
implicit Euler method, qualocation method, Crank-Nicolson scheme, Quadrature, Galerkin Methods, superconvergence, Error bounds for initial value and initial-boundary value problems involving PDEs, collocation method, error estimates, Nonlinear parabolic equations, semilinear parabolic equation, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, time discretization
implicit Euler method, qualocation method, Crank-Nicolson scheme, Quadrature, Galerkin Methods, superconvergence, Error bounds for initial value and initial-boundary value problems involving PDEs, collocation method, error estimates, Nonlinear parabolic equations, semilinear parabolic equation, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, time discretization
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