scholarly journals A Mathematical Model and Numerical Solution of a Boundary Value Problem for a Multi-Structure Plate

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 244 ◽  
Author(s):  
Vildan Yazıcı ◽  
Zahir Muradoğlu
Keyword(s):  
Mathematical Model ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Transmission Conditions ◽  
Numerical Examples ◽  
Deformation Problem ◽  
The Common ◽  
Plate System ◽  
Structure Plate ◽  
Numerical Approaches

This study examined the deformation problem of a plate system (formed side-by-side) composed of multi-structure plates. It obtained numerical approaches of the transmission conditions on the common border of plates that composed the system. Numerical examples were solved in different boundary and transmission conditions.

scholarly journals Mathematical Modelling of Mass Transfer in Zones of Complete and Incomplete Saturation under the Action of Systematic Combined Drainage

2019 ◽  
pp. 86-87
Author(s):  
Anatolii Vlasyuk ◽  
Tatiana Tsvietkova
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Porous Media ◽  
Boundary Value Problem ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Finite Differences ◽  
Unsaturated Porous Media ◽  
Vertical Drains ◽  
The Mathematical Model

The mathematical model of a processes mass transfer in saturated and unsaturated porous media to the filtertrap in isothermal conditions to the system of vertical drains is presented. The numerical solution of the respective boundary value problem was obtained by the method of finite differences using the numerical method of conformal mappings in an inverse statement.

Coupled Fluid-Solid Problems: Survey on Numerical Approaches and Applications

2003 ◽  
Author(s):  
Michael Scha¨fer
Keyword(s):  
Numerical Simulation ◽  
Numerical Solution ◽  
Computational Efficiency ◽  
Numerical Accuracy ◽  
Numerical Examples ◽  
Coupling Mechanisms ◽  
Numerical Approaches

The paper gives a survey on relevant topics related to the numerical simulation of coupled fluid-solid problems. Firstly, the corresponding problems are classified according to different possible coupling mechanisms. The modelling of the problems within a continuum mechanical framework are discussed and numerical aspects related to discretization and solution procedures are addressed. Exemplary approaches for these issues are indicated. A variety of numerical examples involving various coupling mechanisms are presented, including a discussion of questions of numerical accuracy and computational efficiency of numerical solution procedures.

Difference Schemes for Nonlinear BVPS on the Semiaxis

2007 ◽  
Vol 7 (1) ◽  
pp. 25-47 ◽  
Author(s):  
I.P. Gavrilyuk ◽  
M. Hermann ◽  
M.V. Kutniv ◽  
V.L. Makarov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Boundary Value Problem ◽  
Difference Scheme ◽  
Adaptive Algorithm ◽  
Order Differential Equation ◽  
Constructive Method ◽  
Numerical Examples ◽  
Exact Difference ◽  
The Given

Abstract The scalar boundary value problem (BVP) for a nonlinear second order differential equation on the semiaxis is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection of the exact solution of the given differential equation onto the underlying grid. A constructive method is proposed to derive from the EDS a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely selectable natural number. The n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which illustrate the theorems presented in the paper and demonstrate the reliability of the new algorithm.

Photocatalytic Effect of Fe(III) on Oxidation of Two-Carbon Substrates Related to Natural Waters

1994 ◽  
Vol 59 (5) ◽  
pp. 1066-1076 ◽  
Author(s):  
Šárka Klementová ◽  
Dana M. Wagnerová
Keyword(s):  
Mathematical Model ◽  
Natural Waters ◽  
Substrate Oxidation ◽  
Quantum Yields ◽  
Ferric Ions ◽  
Photochemical Reduction ◽  
Photocatalytic Effect ◽  
Carbon Substrates ◽  
Glyoxalic Acid ◽  
The Common

The influence of ferric ions on photoinitiated reaction of dioxygen with two carbon organic acids, aldehydes and alcohols related to natural waters was demonstrated. Photocatalytic effect of ferric ions, i.e. photochemical reduction of Fe(III) as the catalyst generating step, has been found to be the common principal of these reactions. The overall quantum yields of the reactions are in the range from 0.3 to 1.2. A mathematical model designed for the mechanism of cyclic generation of catalyst in the singlet substrate oxidation by O2 was applied to the system glyoxalic acid + Fe(III); a fair agreement between the simulated and experimental kinetic curves was obtained. The experimental rate constant is 4.4 .10-4 s -1.

scholarly journals Identical Limb Dynamics for Unilateral Impairments through Biomechanical Equivalence

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 705
Author(s):  
Fatemeh Rasouli ◽  
Kyle B. Reed
Keyword(s):  
Mathematical Model ◽  
Numerical Solution ◽  
Dynamic Models ◽  
Assistive Devices ◽  
Assistive Device ◽  
Human Walking ◽  
Physical Parameters ◽  
Gait Rehabilitation ◽  
And Performance ◽  
Two Sides

Dynamic models, such as double pendulums, can generate similar dynamics as human limbs. They are versatile tools for simulating and analyzing the human walking cycle and performance under various conditions. They include multiple links, hinges, and masses that represent physical parameters of a limb or an assistive device. This study develops a mathematical model of dissimilar double pendulums that mimics human walking with unilateral gait impairment and establishes identical dynamics between asymmetric limbs. It introduces new coefficients that create biomechanical equivalence between two sides of an asymmetric gait. The numerical solution demonstrates that dissimilar double pendulums can have symmetric kinematic and kinetic outcomes. Parallel solutions with different physical parameters but similar biomechanical coefficients enable interchangeable designs that could be incorporated into gait rehabilitation treatments or alternative prosthetic and ambulatory assistive devices.

scholarly journals A study on multiterm hybrid multi-order fractional boundary value problem coupled with its stability analysis of Ulam–Hyers type

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed Nouara ◽  
Abdelkader Amara ◽  
Eva Kaslik ◽  
Sina Etemad ◽  
Shahram Rezapour ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Boundary Value Problem ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Research Work ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Numerical Examples ◽  
Fractional Derivatives And Integrals ◽  
Fractional Differential

AbstractIn this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed hybrid fractional differential equation that involves Riemann–Liouville fractional derivatives and integrals of multi-orders type are derived using Dhage’s technique, which deals with a composition of three operators. After that, its stability analysis of Ulam–Hyers type and the relevant generalizations are checked. Some illustrative numerical examples are provided at the end to illustrate and validate our obtained results.

scholarly journals Barycentric prolate interpolation and pseudospectral differentiation

2021 ◽  
Author(s):  
Yan Tian
Keyword(s):  
Boundary Value Problem ◽  
Convergence Rates ◽  
Boundary Value ◽  
High Accuracy ◽  
Second Order ◽  
New Method ◽  
Numerical Examples ◽  
Helmholtz Problem ◽  
Collocation Scheme

AbstractIn this paper, we provide further illustrations of prolate interpolation and pseudospectral differentiation based on the barycentric perspectives. The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.

scholarly journals Second-order neutrosophic boundary-value problem

2021 ◽  
Author(s):  
Sandip Moi ◽  
Suvankar Biswas ◽  
Smita Pal(Sarkar)
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Differential Calculus ◽  
Boundary Value ◽  
Second Order ◽  
Numerical Examples ◽  
Different Types ◽  
First Time

AbstractIn this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed. This is the first time where a second-order neutrosophic boundary-value problem has been introduced with different types of first- and second-order derivatives. Some numerical examples have been examined to explain different systems of neutrosophic differential equation.

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

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