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Author:   G. A. Mikhailov
Publisher:   Brill
Imprint:   VSP International Science Publishers
Weight:   0.450kg
ISBN:  

9789067641906

ISBN 10:   9067641901
Pages:   186
Publication Date:   March 1995
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

ESTIMATION OF INTEGRALS AND SOLUTION OF INTEGRAL EQUATIONS Estimation of integrals Recurrent estimates of Monte Carlo method for the solution to an integral equation of the second kind Variance of the basic unbiased estimate Branching chains and solutions to nonlinear equations Cost of various algorithms or solving integral equations Solving problems with stochastic parameters ESTIMATION OF DERIVATIVES Vector Monte Carlo algorithms Calculation derivatives and perturbations with respect to parameters Calculation of parametric derivatives in a special case SOLUTION OF THE HELMHOLTZ EQUATION The 'walk on spheres' process The use of probabilistic representation The use of integral representations New algorithms for variable c(r) 'Walk on spheres' algorithms for solving Helmholtz equation in the n-dimensional space Solving difference equations by the Monte Carlo method Additional remarks SOLUTION OF METAHARMONIC EQUATIONS AND ELLIPTIC SYSTEMS Solution of metaharmonic equations by calculating the parametric derivatives Solving metaharmonic equations of the form p+1u+cu=(-1)p+1g Two-dimensional case Calculation of the covariance function of the solution to the biharmonic equation Monte Carlo solution of Dirichlet problem for elliptic systems with variable parameters MONTE CARLO METHODS WITH CALCULATING PARAMETRIC DERIVATIVES IN THE RADIATION TRANSPORT THEORY Monovelocity transfer process Calculations of derivatives and perturbations Multivelocity radiation transport process with fission Calculation the derivatives with respect to cross-sections Calculating critical values of the parameters: the critical density, the time constant of particle multiplication, the effective multiplication factor Numerical examples Monte Carlo calculations of critical systems with equalization of generations Solving some inverse and stochastic problems of the transfer theory The 'free-path' estimate for solving the transfer equation in total SOLUTION OF NONLINEAR INTEGRAL EQUATIONS Solution of nonlinear integral equations Solution of Dirichlet problem for elliptic equations Minimization of cost of Monte Carlo methods in iterative solution of nonlinear problems Iterative solution of a model kinetic equation Appendix: Some simulation algorithms Numerical simulation of random variables Numerical simulation of random fields Remarks about simulation algorithms with the use of multiprocessor systems References \ authors

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