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We consider the symmetric schemes in Boundary Value Methods (BVMs) applied to delay differential equations y′(t)=ay(t)+by(t-τ) with real coefficients a and b. If the numerical solution tends to zero whenever the exact solution does, the symmetric scheme with (k1+m,k2)-boundary conditions is called τk1,k2(0)-stable. Three families of symmetric schemes, namely the Extended Trapezoidal Rules of first (ETRs) and second (ETR2s) kind, and the Top Order Methods (TOMs), are considered in this paper.By using the boundary locus technology, the delay-dependent stability region of the symmetric schemes are analyzed and their boundaries are found. Then by using a necessary and sufficient condition, the considered symmetric schemes are proved to be τν,ν-1(0)-stable. 相似文献
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In this paper we define an efficient implementation of Runge–Kutta methods of Radau IIA type, which are commonly used when solving stiff ODE-IVPs problems. The proposed implementation relies on an alternative low-rank formulation of the methods, for which a splitting procedure is easily defined. The linear convergence analysis of this splitting procedure exhibits excellent properties, which are confirmed by its performance on a few numerical tests. 相似文献
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We combine fourth‐order boundary value methods (BVMs) for discretizing the temporal variable with fourth‐order compact difference scheme for discretizing the spatial variable to solve one‐dimensional heat equations. This class of new compact difference schemes achieve fourth‐order accuracy in both temporal and spatial variables and are unconditionally stable due to the favorable stability property of BVMs. Numerical results are presented to demonstrate the accuracy and efficiency of the new compact difference scheme, compared to the standard second‐order Crank‐Nicolson scheme. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 846–857, 2003. 相似文献
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Based on high-order linear multistep methods (LMMs), we use the class
of extended trapezoidal rules (ETRs) to solve boundary value problems of ordinary
differential equations (ODEs), whose numerical solutions can be approximated by
boundary value methods (BVMs). Then we combine this technique with fourth-order
Padé compact approximation to discrete 2D Schrödinger equation. We propose a
scheme with sixth-order accuracy in time and fourth-order accuracy in space. It is
unconditionally stable due to the favourable property of BVMs and ETRs. Furthermore,
with Richardson extrapolation, we can increase the scheme to order 6 accuracy
both in time and space. Numerical results are presented to illustrate the accuracy of
our scheme. 相似文献
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