In this article, Modified Backward Euler Scheme is developed to solve the diffusion equation subject to nonlinear nonlocal boundary conditions. The proposed scheme is derived by combining a fourth-order compact finite difference formula in space and a backward differ- entiation for the time derivative term. Nonlinear terms in boundary conditions are linearized by Taylor expansion. Numerical examples are provided to verify the accuracy and efficiency of our proposed method.
{"title":"A MODIFIED BACKWARD EULER SCHEME FOR THE DIFFUSION EQUATION SUBJECT TO NONLINEAR NONLOCAL BOUNDARY CONDITIONS","authors":"Dehilis Sofiane, Bouziani Abdelfatah, Bensaid Souad","doi":"10.32523/2306-6172-2021-9-3-26-38","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-3-26-38","url":null,"abstract":"In this article, Modified Backward Euler Scheme is developed to solve the diffusion equation subject to nonlinear nonlocal boundary conditions. The proposed scheme is derived by combining a fourth-order compact finite difference formula in space and a backward differ- entiation for the time derivative term. Nonlinear terms in boundary conditions are linearized by Taylor expansion. Numerical examples are provided to verify the accuracy and efficiency of our proposed method.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44733633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-18DOI: 10.32523/2306-6172-2021-9-4-17-25
P. Grinevich, R. A. O. Sciences, Moscow, Russia., L. I. F. T. Physics, Chernogolovka, Lomonosov Moscow State University, Cmap, Cnrs, 'Ecole polytechnique, I. P. Paris, Palaiseau, France.
We study the transmission eigenvalues for the multipoint scatterers of the Bethe- Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions d = 2 and d = 3. We show that for these scatterers: 1) each positive energy E is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex E is an interior transmission eigenvalue of infinite multiplicity. The case of dimension d = 1 is also discussed.
{"title":"TRANSMISSION EIGENVALUES FOR MULTIPOINT SCATTERERS","authors":"P. Grinevich, R. A. O. Sciences, Moscow, Russia., L. I. F. T. Physics, Chernogolovka, Lomonosov Moscow State University, Cmap, Cnrs, 'Ecole polytechnique, I. P. Paris, Palaiseau, France.","doi":"10.32523/2306-6172-2021-9-4-17-25","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-4-17-25","url":null,"abstract":"We study the transmission eigenvalues for the multipoint scatterers of the Bethe- Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions d = 2 and d = 3. We show that for these scatterers: 1) each positive energy E is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex E is an interior transmission eigenvalue of infinite multiplicity. The case of dimension d = 1 is also discussed.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45933507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-01DOI: 10.32523/2306-6172-2021-9-2-88-100
V. Vasin, V. Belyaev
We investigate a linear operator equation of the first kind that is ill-posed in the Hadamard sence. It is assumed that its solution is representable as a sum of smooth and discontinuous components. To construct a stable approximate solutions, we use the modified Tikhonov method with the stabilizing functional as a sum of the Lebesgue norm for the smooth component and a smoothed BV-norm for the discontinuous component. Theorems of exis- tence, uniqueness, and convergence both the regularized solutions and its finite-dimentional approximations are proved. Also, results of numerical experiments are presented.
{"title":"THE MODIFIED TIKHONOV REGULARIZATION METHOD WITH THE SMOOTHED TOTAL VARIATION FOR SOLVING THE LINEAR ILL-POSED PROBLEMS","authors":"V. Vasin, V. Belyaev","doi":"10.32523/2306-6172-2021-9-2-88-100","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-2-88-100","url":null,"abstract":"We investigate a linear operator equation of the first kind that is ill-posed in the Hadamard sence. It is assumed that its solution is representable as a sum of smooth and discontinuous components. To construct a stable approximate solutions, we use the modified Tikhonov method with the stabilizing functional as a sum of the Lebesgue norm for the smooth component and a smoothed BV-norm for the discontinuous component. Theorems of exis- tence, uniqueness, and convergence both the regularized solutions and its finite-dimentional approximations are proved. Also, results of numerical experiments are presented.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45993011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-01DOI: 10.32523/2306-6172-2021-9-2-39-56
Houda Fahim, Olivier Sawadogo, N. Alaa, M. Guedda
This work of applied mathematics with interfaces in bio-physics focuses on the shape identification and numerical modelisation of a single red blood cell shape. The purpose of this work is to provide a quantitative method for interpreting experimental observations of the red blood cell shape under microscopy. In this paper we give a new formulation based on classical theory of geometric shape minimization which assumes that the curvature energy with additional constraints controls the shape of the red blood cell. To minimize this energy under volume and area constraints, we propose a new hybrid algorithm which combines Particle Swarm Optimization (PSO), Gravitational Search (GSA) and Neural Network Algorithm (NNA). The results obtained using this new algorithm agree well with the experimental results given by Evans et al. (8) especially for sphered and biconcave shapes.
{"title":"AN EFFICIENT IDENTIFICATION OF RED BLOOD CELL EQUILIBRIUM SHAPE USING NEURAL NETWORKS","authors":"Houda Fahim, Olivier Sawadogo, N. Alaa, M. Guedda","doi":"10.32523/2306-6172-2021-9-2-39-56","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-2-39-56","url":null,"abstract":"This work of applied mathematics with interfaces in bio-physics focuses on the shape identification and numerical modelisation of a single red blood cell shape. The purpose of this work is to provide a quantitative method for interpreting experimental observations of the red blood cell shape under microscopy. In this paper we give a new formulation based on classical theory of geometric shape minimization which assumes that the curvature energy with additional constraints controls the shape of the red blood cell. To minimize this energy under volume and area constraints, we propose a new hybrid algorithm which combines Particle Swarm Optimization (PSO), Gravitational Search (GSA) and Neural Network Algorithm (NNA). The results obtained using this new algorithm agree well with the experimental results given by Evans et al. (8) especially for sphered and biconcave shapes.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42704654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-01DOI: 10.32523/2306-6172-2021-9-2-12-38
R. Silva, V. Priimenko
A transient wave propagation model is provided as a consequence of a new theory of porous media and wave propagation in saturated poroelastic media. This theory, in the linear case, becomes to be equivalent to the theory proposed by de Boer, R., Ehlers, W. & Liu, Z. in 1993. It leads to a model for the 1-D porous saturated column problem, which after the appropriate establishment of boundary and initial conditions, can be solved analytically with the aid of the Laplace transform concerning time. Numerical experiments are performed to illustrate the behavior of constituents displacement fields. The theory results in having an inertial effect on the motion of solid constituents as commonly expected. However, in contrast to Biot’s theory, is not introduced by the present theory the relative acceleration as an interactive force between solid and fluid constituents to account for the apparent inertial effect.
基于多孔介质和饱和孔弹性介质中波的传播理论，提出了一种瞬态波传播模型。在线性情况下，该理论与de Boer, R.， Ehlers, W. & Liu, Z.在1993年提出的理论等价。建立了一维多孔饱和柱问题的模型，该模型在适当的边界条件和初始条件建立后，可以借助随时间的拉普拉斯变换解析求解。通过数值实验说明了构件位移场的特性。该理论的结果是对固体成分的运动具有惯性效应，这是通常所期望的。然而，与Biot的理论相反，本理论没有引入相对加速度作为固体和流体组分之间的相互作用力来解释表观惯性效应。
{"title":"AN ANALYTICAL SOLUTION OF THE SATURATED AND INCOMPRESSIBLE POROELASTIC MODEL FOR TRANSIENT WAVE PROPAGATION","authors":"R. Silva, V. Priimenko","doi":"10.32523/2306-6172-2021-9-2-12-38","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-2-12-38","url":null,"abstract":"A transient wave propagation model is provided as a consequence of a new theory of porous media and wave propagation in saturated poroelastic media. This theory, in the linear case, becomes to be equivalent to the theory proposed by de Boer, R., Ehlers, W. & Liu, Z. in 1993. It leads to a model for the 1-D porous saturated column problem, which after the appropriate establishment of boundary and initial conditions, can be solved analytically with the aid of the Laplace transform concerning time. Numerical experiments are performed to illustrate the behavior of constituents displacement fields. The theory results in having an inertial effect on the motion of solid constituents as commonly expected. However, in contrast to Biot’s theory, is not introduced by the present theory the relative acceleration as an interactive force between solid and fluid constituents to account for the apparent inertial effect.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43726300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-01DOI: 10.32523/2306-6172-2021-9-2-4-11
Bukalin, Alexey, Zagrebaev Andrey
This paper describes a computer program that implements an algorithm for com- pressing technological information with losses using archive data of the information-measuring system "Skala-micro" of the Kursk and Smolensk NPPs as an example. The presented al- gorithm allows to compress file archives at the data level with the possibility of their quick subsequent recovery within the limits of the acceptable error. The main goal of the algorithm is to significantly reduce the excess amount of memory when storing data for its subsequent more efficient use.
{"title":"NEW DATA COMPRESSION ALGORITHM FOR TECHNOLOGICAL INFORMATION OF THE INFORMATION-MEASURING SYSTEM \"SKALA-MICRO\"","authors":"Bukalin, Alexey, Zagrebaev Andrey","doi":"10.32523/2306-6172-2021-9-2-4-11","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-2-4-11","url":null,"abstract":"This paper describes a computer program that implements an algorithm for com- pressing technological information with losses using archive data of the information-measuring system \"Skala-micro\" of the Kursk and Smolensk NPPs as an example. The presented al- gorithm allows to compress file archives at the data level with the possibility of their quick subsequent recovery within the limits of the acceptable error. The main goal of the algorithm is to significantly reduce the excess amount of memory when storing data for its subsequent more efficient use.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41631268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.32523/2306-6172-2020-8-3-12-32
B. M., Essoufi El-H., A. M.
{"title":"Numerical Analysis Of The Penalty Method For Unilateral Contact Problem With Tresca’s Friction In Thermo-Electro-Visco-Elasticity.","authors":"B. M., Essoufi El-H., A. M.","doi":"10.32523/2306-6172-2020-8-3-12-32","DOIUrl":"https://doi.org/10.32523/2306-6172-2020-8-3-12-32","url":null,"abstract":"","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69698430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.32523/2306-6172-2020-8-4-83-96
B. Rysbaiuly, N. Rysbaeva
The nonlinear model of heat transfer in freezing soil was corrected using the results of experimental studies of other scientists. A nonlinear difference equation is constructed and a priori estimates are obtained for solving nonlinear algebraic equations. The nonlinear difference problem is solved by Newton’s method. The paper also considers the problem of choosing the initial approximation of Newton’s method. Using a priori estimates, the quadratic convergence of the iterative method is proved. Numerical calculations have been performed. A strong discrepancy in results between linear and nonlinear difference problem is shown using graphical representation.
{"title":"THE METHOD OF SOLVING NONLINEAR HEAT TRANSFER MODEL IN FREEZING SOIL","authors":"B. Rysbaiuly, N. Rysbaeva","doi":"10.32523/2306-6172-2020-8-4-83-96","DOIUrl":"https://doi.org/10.32523/2306-6172-2020-8-4-83-96","url":null,"abstract":"The nonlinear model of heat transfer in freezing soil was corrected using the results of experimental studies of other scientists. A nonlinear difference equation is constructed and a priori estimates are obtained for solving nonlinear algebraic equations. The nonlinear difference problem is solved by Newton’s method. The paper also considers the problem of choosing the initial approximation of Newton’s method. Using a priori estimates, the quadratic convergence of the iterative method is proved. Numerical calculations have been performed. A strong discrepancy in results between linear and nonlinear difference problem is shown using graphical representation.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69698513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.32523/2306-6172-2020-8-3-56-66
Galakhov V.P., Lovtskaya O.V., Mardasova E.V.
{"title":"Stochastic Simulation Of Maximum Levels In Biya River.","authors":"Galakhov V.P., Lovtskaya O.V., Mardasova E.V.","doi":"10.32523/2306-6172-2020-8-3-56-66","DOIUrl":"https://doi.org/10.32523/2306-6172-2020-8-3-56-66","url":null,"abstract":"","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69698447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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