scholarly journals Modelling of an explosion impact on a deformable medium with rigid inclusions with quasiconformal mappings methods

2020 ◽  
pp. 19-22
Author(s):  
Kateryna Mykolaiivna Malash ◽  
Andrii Bomba
Keyword(s):  
Numerical Methods ◽  
Numerical Experiments ◽  
Quasiconformal Mappings ◽  
Deformable Medium ◽  
Process Characteristics ◽  
Explosive Process

The explosive process influence on the environment with the existing impenetrable fixed inclusion is investigated by quasiconformal mappings numerical methods and step-by-step parameterization of the environment and the process characteristics numerical methods. The boundaries of the crater formed by the explosion, pressed and undisturbed areas of soil are determined. Numerical experiments were performed on the basis of the developed algorithm

scholarly journals Application of quasiconformal mapping methods to the investigation of the explosive processes impact on the environment

2019 ◽  
pp. 17-18
Author(s):  
Kateryna Mykolaiivna Malash ◽  
Andrii Yaroslavovych Bomba
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Quasiconformal Mapping ◽  
Quasiconformal Mappings ◽  
Practical Application

The mathematical models used to study explosive processes are given. A class of problems investigating the influence of explosive processes on the environment by the quasiconformal mappings numerical methods are outlined and their practical application are described

scholarly journals A Class of New Pouzet-Runge-Kutta-Type Methods for Nonlinear Functional Integro-Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Chengjian Zhang
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
Numerical Stability ◽  
Numerical Experiments ◽  
Integrodifferential Equations ◽  
Stability Criteria ◽  
Nonlinear Functional ◽  
Runge Kutta ◽  
Theoretical Results

This paper presents a class of new numerical methods for nonlinear functional-integrodifferential equations, which are derived by an adaptation of Pouzet-Runge-Kutta methods originally introduced for standard Volterra integrodifferential equations. Based on the nonclassical Lipschitz condition, analytical and numerical stability is studied and some novel stability criteria are obtained. Numerical experiments further illustrate the theoretical results and the effectiveness of the methods. In the end, a comparison between the presented methods and the existed related methods is given.

SYMPLECTIC NUMERICAL METHODS FOR HAMILTONIAN PROBLEMS

1993 ◽  
Vol 04 (02) ◽  
pp. 385-392 ◽  
Author(s):  
J. M. SANZ-SERNA ◽  
M. P. CALVO
Keyword(s):  
Numerical Methods ◽  
Numerical Integration ◽  
Numerical Experiments ◽  
Symplectic Methods ◽  
Hamiltonian Problems ◽  
Integral Invariants

We consider symplectic methods for the numerical integration of Hamiltonian problems, i.e. methods that preserve the Poincaré integral invariants. Examples of symplectic methods are given and numerical experiments are reported.

scholarly journals APPLIED QUASIPOTENTIAL METHOD FOR SOLVING THE COEFFICIENT PROBLEMS OF PARAMETER IDENTIFICATION OF ANISOTROPIC MEDIA

2019 ◽  
Vol 9 (1) ◽  
pp. 33-36 ◽  
Author(s):  
Andrii Bomba ◽  
Andrij Safonyk ◽  
Olha Michuta ◽  
Mykhailo Boichura
Keyword(s):  
Parameter Identification ◽  
Numerical Method ◽  
Anisotropic Medium ◽  
Numerical Experiments ◽  
Anisotropic Media ◽  
Quasiconformal Mappings ◽  
Conductivity Tensor ◽  
Coefficient Problems ◽  
Tomographic Data

A numerical method of quasiconformal mappings for solving the coefficient problems of finding eigenvalues of the conductivity tensor having information about its directions in an anisotropic medium using applied quasipotential tomographic data is generalized. The corresponding algorithm is based on the alternate solving of problems on quasiconformal mappings and parameter identification. The results of numerical experiments of imitative restoration of environment structure are presented.

Element removal method for singular minimizers in variational problems involving Lavrentiev phenomenon

1992 ◽  
Vol 439 (1905) ◽  
pp. 131-137 ◽  
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
Numerical Experiments ◽  
Variational Problems ◽  
Lavrentiev Phenomenon ◽  
Removal Method ◽  
Element Removal Method ◽  
Element Removal ◽  
Singular Minimizers

A numerical method called element removal method is designed to calculate singular minimizers which cannot be approximated by simple applications of standard numerical methods because of the so-called Lavrentiev phenomenon. The convergence of the method is proved. The results of numerical experiments show that the method is effective.

scholarly journals Symplectic Effective Order Numerical Methods for Separable Hamiltonian Systems

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 142 ◽  
Author(s):  
Junaid Ahmad ◽  
Yousaf Habib ◽  
Shafiq Rehman ◽  
Azqa Arif ◽  
Saba Shafiq ◽  
...  
Keyword(s):  
Hamiltonian System ◽  
Numerical Methods ◽  
Energy Conservation ◽  
Hamiltonian Systems ◽  
Numerical Experiments ◽  
Effective Order ◽  
Good Energy ◽  
Runge Kutta ◽  
Separable Hamiltonian System ◽  
Selection Of

A family of explicit symplectic partitioned Runge-Kutta methods are derived with effective order 3 for the numerical integration of separable Hamiltonian systems. The proposed explicit methods are more efficient than existing symplectic implicit Runge-Kutta methods. A selection of numerical experiments on separable Hamiltonian system confirming the efficiency of the approach is also provided with good energy conservation.

Two New Energy-Preserving Algorithms for Generalized Fifth-Order KdV Equation

2017 ◽  
Vol 9 (5) ◽  
pp. 1206-1224 ◽  
Author(s):  
Qi Hong ◽  
Yushun Wang ◽  
Qikui Du
Keyword(s):  
Vector Field ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
Numerical Experiments ◽  
Kdv Equation ◽  
Field Method ◽  
Local Energy ◽  
New Energy ◽  
Vector Field Method ◽  
Fifth Order

AbstractIn this paper, based on the multi-symplectic formulations of the generalized fifth-order KdV equation and the averaged vector field method, two new energy-preserving methods are proposed, including a new local energy-preserving algorithm which is independent of the boundary conditions and a new global energy-preserving method. We prove that the proposed methods preserve the energy conservation laws exactly. Numerical experiments are carried out, which demonstrate that the numerical methods proposed in the paper preserve energy well.

A Comparison Study of Numerical Methods for Compressible Two-Phase Flows

2017 ◽  
Vol 9 (5) ◽  
pp. 1111-1132 ◽  
Author(s):  
Jianyu Lin ◽  
Hang Ding ◽  
Xiyun Lu ◽  
Peng Wang
Keyword(s):  
Numerical Methods ◽  
Numerical Experiments ◽  
Mass Conservation ◽  
Detailed Comparison ◽  
Equation Model ◽  
Bubble Collapse ◽  
Comparison Study ◽  
Two Phase Flows ◽  
Two Phase ◽  
Interface Position

AbstractIn this article a comparison study of the numerical methods for compressible two-phase flows is presented. Although many numerical methods have been developed in recent years to deal with the jump conditions at the fluid-fluid interfaces in compressible multiphase flows, there is a lack of a detailed comparison of these methods. With this regard, the transport five equation model, the modified ghost fluid method and the cut-cell method are investigated here as the typical methods in this field. A variety of numerical experiments are conducted to examine their performance in simulating inviscid compressible two-phase flows. Numerical experiments include Richtmyer-Meshkov instability, interaction between a shock and a rectangle SF6 bubble, Rayleigh collapse of a cylindrical gas bubble in water and shock-induced bubble collapse, involving fluids with small or large density difference. Based on the numerical results, the performance of the method is assessed by the convergence order of the method with respect to interface position, mass conservation, interface resolution and computational efficiency.

The formulation and analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein–Gordon equations

2018 ◽  
Vol 39 (4) ◽  
pp. 2016-2044 ◽  
Author(s):  
Bin Wang ◽  
Xinyuan Wu
Keyword(s):  
Numerical Methods ◽  
Global Convergence ◽  
Nonlinear Stability ◽  
Numerical Experiments ◽  
High Dimensional ◽  
Local Error ◽  
Discrete Gradient Method ◽  
New Energy ◽  
Klein Gordon ◽  
Duhamel Principle

Abstract In this paper we focus on the analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein–Gordon equations. A novel energy-preserving scheme is developed based on the discrete gradient method and the Duhamel principle. The local error, global convergence and nonlinear stability of the new scheme are analysed in detail. Numerical experiments are implemented to compare with existing numerical methods in the literature, and the numerical results show the remarkable efficiency of the new energy-preserving scheme presented in this paper.

scholarly journals Numerical Methods for a Class of Differential Algebraic Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Lei Ren ◽  
Yuan-Ming Wang
Keyword(s):  
Numerical Methods ◽  
Constant Coefficient ◽  
Numerical Experiments ◽  
Inverse Method ◽  
Padé Approximation ◽  
Differential Algebraic Equations ◽  
Drazin Inverse ◽  
Time Varying ◽  
Algebraic Equations ◽  
Pade Approximation

This paper is devoted to the study of some efficient numerical methods for the differential algebraic equations (DAEs). At first, we propose a finite algorithm to compute the Drazin inverse of the time varying DAEs. Numerical experiments are presented by Drazin inverse and Radau IIA method, which illustrate that the precision of the Drazin inverse method is higher than the Radau IIA method. Then, Drazin inverse, Radau IIA, and Padé approximation are applied to the constant coefficient DAEs, respectively. Numerical results demonstrate that the Padé approximation is powerful for solving constant coefficient DAEs.

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