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2010年09月28日

【期刊论文】Methods with high accuracy for finite element probability computing

彭龙， Peng Long a， *， Wang Jinliang b， Zhu Qiding a

Journal of Computational and Applied Mathematics 59 (1995) 181-189，-0001，（）：

-1年11月30日

摘要

This paper introduces methods with high accuracy for finite element probability computing, by which the function value on one or a few nodes can be calculated without forming the total stiffness matrix.

Finite element， Mathematical expectation， Random walk， Multi-grid， Probability computing method

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2010年09月28日

【期刊论文】MULTILEVEL CORRECTION FOR COLLOCATION SOLUTIONS OF VOLTERRA NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS*

彭龙， HU Qiya， PENG Long

Systerns Science and Mathematical Sciences Apr., 2000 Vol.13 No.2，-0001，（）：

-1年11月30日

摘要

In this paper we give a complete analysis of the convergence acceleration method for collocation solutions of Volterra nonlinear integro-differential equations with smooth kernels. It will be shown that when continuous piecewise polynomials of degree m are used and collocation is based on the Lobatto points, the first derivative of this collocation approximation admits, at the knots, an error expansion in even powers of the step-size h, beginning with a term in h2m, On the basis of this expansion we show that when a correction procedure is applied to this collocation approximation for k times: the global accurary of the corresponding corrected approximation will be increased to O(h2m(k+1).

Nonlinear integro-differential equation， collocation solution， error expansion， multilevel correction