Convergence theory for spectral deferred correction
نویسندگان
چکیده
In a recent article [2] Dutt, Greengard and Rohklin define two newmethods of deferred correction. Convergence for the the first method, using one step methods, has been proven in Hansen [8]. In this paper we augment the theory presented in [8] and use this to prove convergence for the second deferred correction method in [2] using linear k-step methods. This method has been known as Spectral Deferred Correction.
منابع مشابه
Comments on High Order Integrators Embedded within Integral Deferred Correction Methods
Spectral deferred correction (SDC) methods for solving ordinary differential equations (ODEs) were introduced by Dutt, Greengard and Rokhlin, [3]. In this paper, we study the properties of these integral deferred correction methods, constructed using high order integrators in the prediction and correction loops, and various distributions of quadrature nodes. The smoothness of the error vector a...
متن کاملAccelerating the convergence of spectral deferred correction methods
In the recent paper by Dutt, Greengard and Rokhlin, a variant of deferred or defect correction methods is presented which couples Gaussian quadrature with the Picard integral equation formulation of the initial value ordinary differential equation. The resulting spectral deferred correction methods (SDC) have been shown to possess favorable accuracy and stability properties even for versions wi...
متن کاملAn enhanced parareal algorithm based on the deferred correction methods for a stiff system
In this study, we consider a variant of the hybrid parareal algorithm based on deferred correction techniques in order to increase the convergence order even for the stiff system. A hybrid parareal scheme introduced by Minion (2011) [20] improves the efficiency of the original parareal by utilizing a Spectral Deferred Correction (SDC) strategy for a fine propagator within the parareal iteration...
متن کاملEfficient High-order Rational Integration and Deferred Correction with Equispaced Data
Stable high-order linear interpolation schemes are well suited for the accurate approximation of antiderivatives and the construction of efficient quadrature rules. In this paper we utilize for this purpose the family of linear barycentric rational interpolants by Floater and Hormann, which are particularly useful for interpolation with equispaced nodes. We analyze the convergence of integrals ...
متن کاملConservative Multi-Implicit Spectral Deferred Correction Methods for Reacting Gas Dynamics ?
In most models of reacting gas dynamics, the characteristic time scales of chemical reactions are much shorter than the hydrodynamic and diffusive time scales, rendering the reaction part of the model equations stiff. Moreover, nonlinear forcings may introduce into the solutions sharp gradients or shocks, the robust behavior and correct propagation of which require the use of specialized spatia...
متن کامل