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【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
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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彭龙, HU Qiya, PENG Long
Systerns Science and Mathematical Sciences Apr., 2000 Vol.13 No.2,-0001,():
-1年11月30日
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
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