Solution of Initial-Boundary Value Problems : Method of Moving Modes

Umurdin Dalabaev

ISBN 10: 3111304396 / ISBN 13: 9783111304397

Edité par De Gruyter, 2025

A propos de cet article

Neuware - Methods for solving problems of mathematical physics can be divided into the following four classes. Analytical methods (the method of separation of variables, the method of characteristics, the method of Green's functions, etc.) methods have a relatively low degree of universality, i.e. focused on solving rather narrow classes of problems. Approximate analytical methods (projection, variational methods, small parameter method, operational methods, various iterative methods) are more versatile than analytical ones. Numerical methods (finite difference method, direct method, control volume method, finite element method, etc.) are very universal methods. Probabilistic methods (Monte Carlo methods) are highly versatile. Can be used to calculate discontinuous solutions. However, they require large amounts of calculations and, as a rule, they lose with the computational complexity of the above methods when solving such problems to which these methods are applicable. Comparing methods for solving problems of mathematical physics, it is impossible to give unconditional primacy to any of them. Any of them may be the best for solving problems of a certain class. The proposed method of moving nodes for boundary value problems of differential equations combines a combination of numerical and analytical methods. In this case, we can obtain, on the one hand, an approximately analytical solution of the problem, which is not related to the methods listed above. On the other hand, this method allows one to obtain compact discrete approximations of the original problem. Note that obtaining an approximately analytical solution of differential equations is based on numerical methods. The nature of numerical methods also allows obtaining an approximate analytical expression for solving differential equations.

N° de réf. du vendeur 9783111304397

Détails bibliographiques

• Titre: Solution of Initial-Boundary Value Problems : Method of Moving Modes
• Éditeur: De Gruyter
• Date de parution: 2025
• Langue: anglais
• ISBN à 10 chiffres: 3111304396
• ISBN à 13 chiffres: 9783111304397
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 240 L x 170 H x 36 P (en millimètres) 240 millimètres de largeur par 170 millimètres de hauteur par 36 millimètres de profondeur
• Poids: 370 grammes

A propos de ce titre

Synopsis

Methods for solving problems of mathematical physics can be divided into the following four classes.

Analytical methods (the method of separation of variables, the method of characteristics, the method of Green's functions, etc.) methods have a relatively low degree of universality, i.e. focused on solving rather narrow classes of problems.

Approximate analytical methods (projection, variational methods, small parameter method, operational methods, various iterative methods) are more versatile than analytical ones.

Numerical methods (finite difference method, direct method, control volume method, finite element method, etc.) are very universal methods.

Probabilistic methods (Monte Carlo methods) are highly versatile. Can be used to calculate discontinuous solutions. However, they require large amounts of calculations and, as a rule, they lose with the computational complexity of the above methods when solving such problems to which these methods are applicable.

Comparing methods for solving problems of mathematical physics, it is impossible to give unconditional primacy to any of them. Any of them may be the best for solving problems of a certain class.

The proposed method of moving nodes for boundary value problems of differential equations combines a combination of numerical and analytical methods. In this case, we can obtain, on the one hand, an approximately analytical solution of the problem, which is not related to the methods listed above. On the other hand, this method allows one to obtain compact discrete approximations of the original problem. Note that obtaining an approximately analytical solution of differential equations is based on numerical methods. The nature of numerical methods also allows obtaining an approximate analytical expression for solving differential equations

À propos de l?auteur

Umurdin Dalabaev, University of World Economy and Diplomacy, Uzbekistan.