Monte Carlo method for linear and nonlinear boundary value problems : Foundation, algorithms, numerical solutions and applications

Abdujabar Rasulov

ISBN 10: 384541183X / ISBN 13: 9783845411835

Published by LAP LAMBERT Academic Publishing, 2011

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - Availability of multiprocessor computers, allows us to solve many complex problems using Monte Carlo method. Monte Carlo methods have been further developed to solve a variety of multidimensional integrals, linear and nonlinear boundary value problems. In monograph we used the deep connections between differential equations and random processes. This connection has been known long ago, the results of the theory of differential equations have been widely used in the theory of probability and vice versa. The solutions of large class linear and nonlinear equations of elliptic and parabolic type may be represented in the form of integrals over the trajectories of Markov process. In the current work we study the approaches connected with simple and branching Markov processes. We obtained effective unbiased estimators for the solutions. Constructed numerical algorithms are strict proved and used for the solution of problems of mathematical physics. This book meant for specialists of numerical methods who applied Monte Carlo methods for the solution boundary value problems, calculating multidimensional integrals and work in the area financial mathematics and statistics.

Seller Inventory # 9783845411835

Bibliographic Details

• Title: Monte Carlo method for linear and nonlinear boundary value problems : Foundation, algorithms, numerical solutions and applications
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2011
• Language: English
• ISBN 10: 384541183X
• ISBN 13: 9783845411835
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 17D millimeters 220 millimeters width by 150 millimeters height by 17 millimeters depth
• Weight: 417 grams

About this title

Synopsis

Availability of multiprocessor computers, allows us to solve many complex problems using Monte Carlo method. Monte Carlo methods have been further developed to solve a variety of multidimensional integrals, linear and nonlinear boundary value problems. In monograph we used the deep connections between differential equations and random processes. This connection has been known long ago, the results of the theory of differential equations have been widely used in the theory of probability and vice versa. The solutions of large class linear and nonlinear equations of elliptic and parabolic type may be represented in the form of integrals over the trajectories of Markov process. In the current work we study the approaches connected with simple and branching Markov processes. We obtained effective unbiased estimators for the solutions. Constructed numerical algorithms are strict proved and used for the solution of problems of mathematical physics. This book meant for specialists of numerical methods who applied Monte Carlo methods for the solution boundary value problems, calculating multidimensional integrals and work in the area financial mathematics and statistics.

About the Author

Professor, Field of study: Monte Carlo methods and asynchronous algorithms. Head of Department Mathematical Modeling and Informatics,University of World Economy and Diplomacy (UWED). Co-autor: Gulnora Raimova, Field of study: Monte Carlo methods. Associate professor of Department Mathematical Modeling and Informatics, UWED,Tashkent,Uzbekistan