[PDF] Top 20 Avoiding order reduction when integrating linear initial boundary value problems with Lawson methods

... classical methods which do have stages, such as Runge- Kutta, Fractional-Step-Runge-Kutta, Runge-Kutta-Nystr¨ om or Rosenbrock methods, some techniques have been suggested in the literature to avoid ... See full document

... type boundary conditions are not considered, parabolic prob- lems for which a summation-by-parts argument can be applied are not included and finally, Lie-Trotter method is not ...avoid order ... See full document

... (1) with Strang method in such a way that order reduction is completely ...avoid order reduc- tion with Runge-Kutta type methods when integrating linear ... See full document

... time when integrating problem (37) with exact solution u(x, t) = e x−t , using second-order finite differences in space and, in time, the classical approach of Gaussian rule with s = 2 ... See full document

... exponential methods when integrating linear initial bound- ary value parabolic problems under homogeneous Dirichlet boundary ...that order reduction ... See full document

... [?] when integrating regular solutions of Schr¨ odinger ...tional order of convergence and summation by parts appear in the case of C 0 -semigroups and Runge-Kutta type methods ... See full document

... Remark 3. It is interesting to observe that, even if (5) is somewhat too restric- tive, some condition regarding the growth of h with respect to u 0 is required. We may recall, for instance, the following example ... See full document

... to linear and nonlinear meromorphic ODEs has been discovered two decades ago, see for instance [–], but in the framework of PDEs very few results are ...the linear case in two complex variables ... See full document

... sector with small radius centered at 0 and a strip in C 2 , that is a solution of the equation (113) and which is the common Gevrey asymptotic expansion of order 1/k of the actual solutions u p (t, z, ) of ... See full document

... in order the minimize the estimation error of the model’s parameters when initial sales information is available, compared to that proposed by [9] based on linear ... See full document

... In order to deal with the problem ...integral. With the help of Henstock–Kurzweil–Stieltjes integrals, we establish the existence and uniqueness of solutions for the second order DDE ... See full document

... space-time methods which employ finite element discretization of the time domain as well as the usual discretization of the spatial ...radiation boundary conditions [1, 2, 3, 4] in an adaptive space- time ... See full document

... These Banach spaces are slight modifications of those introduced in the former work [17] of the second author. The next proposition will be stated without proof since it follows exactly the same steps as in Proposition ... See full document

... increases with the iteration ...gains when the number of iterations that are required for con- vergence is large enough to increment notoriously the size of the factors, as is the case for the two ... See full document

... associated with weak elastostatic shocks in the limit k → ...shocks with strength ...α with the initial fibre direction for a given material characterised by ... See full document

... The number of columns of factor ˜ 𝑆 is doubled at each iteration and, in con- sequence, the computational and storage costs associated with its update grow at each iteration. To moderate this increase, and the ... See full document

... In [6] a random walk was proposed, in the case N = 1, which has the property that if the initial condition has compact support, then the spacial support of the solution is compact for any t > 0. This was ... See full document

... connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now ... See full document

... In this work, we consider the mixed method of Hellinger and Reissner and impose the Neumann boundary condition in a strong sense. Then, we follow [4, 5] and add appropriate Galerkin least- squares type terms. In ... See full document

... We now give a general overview of the sections in which the present study is divided and the main results obtained. The statement of the main problem under consideration is settled in Sect. 2, where we give arguments on ... See full document