Differential-algebraic equations (DAE’s) arise naturally in many applied fields, but numerical and analytical difficulties that have not appeared in ordinary differential equations (ODE’s) occur in DAE’s because it...
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Differential-algebraic equations (DAE’s) arise naturally in many applied fields, but numerical and analytical difficulties that have not appeared in ordinary differential equations (ODE’s) occur in DAE’s because it includes algebraic constrained equations. Some efficient numerical methods for ODE’s can not work well for DAE’s. So many eminent numerical analysis scholars are interested in this field recently. But few numerical methods are able to solve all DAE’s because of its essential difficulties. This paper discusses the simulation algorithm character of DAE’s. And we construct an efficient constrained-algebraic algorithm based on the Runge-Kutta methods of order two for the semi-explicit differential-algebraic equations with index two and give the computational experiment results for specific examples. The experiment results indicate that the constrained-algebraic algorithm is high efficient for semi-explicit differential-algebraic equations with index two.
In this paper, we obtain H1 norm estimate for multigrid method for plate bending problem. Meanwhile, optimal convergence rate under H1 norm is also obtainted for nested iteration multigrid method.
In this paper, we obtain H1 norm estimate for multigrid method for plate bending problem. Meanwhile, optimal convergence rate under H1 norm is also obtainted for nested iteration multigrid method.
The main purpose of this paper is to develop and simplify the general conditions for an s-stage explicit canonical difference scheme of q-th order, while the simplified order conditions for canonical RKN methods which...
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The main purpose of this paper is to develop and simplify the general conditions for an s-stage explicit canonical difference scheme of q-th order, while the simplified order conditions for canonical RKN methods which are applied to a special kind of second order ordinary differential equations are also obtained here.
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