The time-dependent Laplace-type equation of variable coefficients for anisotropic inhomogeneous media is discussed in this paper. Numerical solutions to problems which are governed by the equation are sought by using a combined Laplace transform and boundary element method. The variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation after being Laplace transformed is then written in a boundary-only integral equation involving a time-free fundamental solution. The boundary integral equation is therefore employed to find the numerical solutions using a standard boundary element method. Finally the numerical results are inversely transformed numerically using the Stehfest formula to obtain solutions in the time variable. Some problems of anisotropic functionally graded media are considered. The results show that the combined Laplace transform and boundary element method is accurate and easy to implement.
{"title":"Numerical solutions for 2D unsteady Laplace-Type Problems of anisotropic functionally Graded materials","authors":"M. Azis","doi":"10.3846/mma.2022.14463","DOIUrl":"https://doi.org/10.3846/mma.2022.14463","url":null,"abstract":"The time-dependent Laplace-type equation of variable coefficients for anisotropic inhomogeneous media is discussed in this paper. Numerical solutions to problems which are governed by the equation are sought by using a combined Laplace transform and boundary element method. The variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation after being Laplace transformed is then written in a boundary-only integral equation involving a time-free fundamental solution. The boundary integral equation is therefore employed to find the numerical solutions using a standard boundary element method. Finally the numerical results are inversely transformed numerically using the Stehfest formula to obtain solutions in the time variable. Some problems of anisotropic functionally graded media are considered. The results show that the combined Laplace transform and boundary element method is accurate and easy to implement.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85486297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces. Strong convergence theorems of the suggested iterative schemes are established without the prior knowledge of the Lipschitz constant of the mapping. Finally, some numerical examples are provided to illustrate the efficiency and advantages of the proposed algorithms and compare them with some related ones.
{"title":"Self adaptive viscosity-Type inertial extragradient Algorithms for solving variational inequalities with Applications","authors":"Bing Tan, X. Qin","doi":"10.3846/mma.2022.13846","DOIUrl":"https://doi.org/10.3846/mma.2022.13846","url":null,"abstract":"In this paper, we introduce two new inertial extragradient algorithms with non-monotonic stepsizes for solving monotone and Lipschitz continuous variational inequality problems in real Hilbert spaces. Strong convergence theorems of the suggested iterative schemes are established without the prior knowledge of the Lipschitz constant of the mapping. Finally, some numerical examples are provided to illustrate the efficiency and advantages of the proposed algorithms and compare them with some related ones.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83701375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Dullin-Gottwald-Holm equation models the unidirectional propagation of shallow regime water waves. In this work, the Lie symmetry analysis of the generalised two-component modified weakly dissipative Dullin-Gottwald-Holm system is performed. Using symmetry reduction, the exact solutions are obtained in the form of power series and trigonometric functions. Also using multiplier approach, the conservation laws are obtained. The 3D graphical representations are also shown for obtained solutions.
{"title":"Generalised two-Component modified Weakly dissipative Dullin-Gottwald-Holm System: invariance Analysis and conservation Laws","authors":"S Kumar, D. Jyoti","doi":"10.3846/mma.2022.14249","DOIUrl":"https://doi.org/10.3846/mma.2022.14249","url":null,"abstract":"The Dullin-Gottwald-Holm equation models the unidirectional propagation of shallow regime water waves. In this work, the Lie symmetry analysis of the generalised two-component modified weakly dissipative Dullin-Gottwald-Holm system is performed. Using symmetry reduction, the exact solutions are obtained in the form of power series and trigonometric functions. Also using multiplier approach, the conservation laws are obtained. The 3D graphical representations are also shown for obtained solutions.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74581498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we concentrate on a class of time-fractional diffusion and subdiffusion equations. To solve the mentioned problems, we construct twodimensional Genocchi-fractional Laguerre functions (G-FLFs). Then, the pseudooperational matrices are used to convert the proposed equations to systems of algebraic equations. The properties of pseudo-operational matrices have reflected well in the process of the numerical technique and create an approximate solution with high precision. Finally, several examples are presented to illustrate the accuracy and effectiveness of the technique.
{"title":"A spectral Approach for Time-fractional diffusion and subdiffusion equations in a Large interval","authors":"Haniye Dehestani, Y. Ordokhani, M. Razzaghi","doi":"10.3846/mma.2022.13579","DOIUrl":"https://doi.org/10.3846/mma.2022.13579","url":null,"abstract":"In this paper, we concentrate on a class of time-fractional diffusion and subdiffusion equations. To solve the mentioned problems, we construct twodimensional Genocchi-fractional Laguerre functions (G-FLFs). Then, the pseudooperational matrices are used to convert the proposed equations to systems of algebraic equations. The properties of pseudo-operational matrices have reflected well in the process of the numerical technique and create an approximate solution with high precision. Finally, several examples are presented to illustrate the accuracy and effectiveness of the technique.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73804100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we develop a monotone iterative technique (MI-technique) with lower and upper (L-U) solutions for a class of four-point Dirichlet nonlinear boundary value problems (NLBVPs), defined as, ... where ..., ... the non linear term ...is continuous function in x, one sided Lipschitz in ψ and Lipschitz in . To show the existence result, we construct Green’s function and iterative sequences for the corresponding linear problem. We use quasilinearization to construct these iterative schemes. We prove maximum principle and establish monotonicity of sequences of lower solution and upper solution such that... Then under certain sufficient conditions we prove that these sequences converge uniformly to the solution ψ(x) in a specific region where
{"title":"Well Ordered Monotone iterative Technique for nonlinear second order Four Point Dirichlet BVPs","authors":"Amit Verma, Nazia Urus","doi":"10.3846/mma.2022.14198","DOIUrl":"https://doi.org/10.3846/mma.2022.14198","url":null,"abstract":"In this article, we develop a monotone iterative technique (MI-technique) with lower and upper (L-U) solutions for a class of four-point Dirichlet nonlinear boundary value problems (NLBVPs), defined as, ... where ..., ... the non linear term ...is continuous function in x, one sided Lipschitz in ψ and Lipschitz in . To show the existence result, we construct Green’s function and iterative sequences for the corresponding linear problem. We use quasilinearization to construct these iterative schemes. We prove maximum principle and establish monotonicity of sequences of lower solution and upper solution such that... Then under certain sufficient conditions we prove that these sequences converge uniformly to the solution ψ(x) in a specific region where","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83463535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shielding properties of a cylindrical thick-walled ferrofluid layer that protects against externally applied uniform magnetic fields are numerically investigated. We take into account the diffusion of magnetic nanoparticles in the ferrofluid with magnetic dipole-dipole, steric and hydrodynamic interactions between particles. Permeability of the ferrofluid is considered to be dependent on the magnetic-field strength and the particle concentration. A combined method of finite differences and boundary elements is applied to solve a nonlinear transmission problem of magnetostatics in the whole space, augmented by nonlinear algebraic equations based on the mass transfer equation for magnetic nanoparticles in ferrofluids. Numerical experiments revealed that the diffusion of particles has negligible influence on the shielding properties at weak and strong intensities of the applied magnetic field when comparing with the results of computations for a uniform particle distribution.
{"title":"Numerical Study of the shielding Properties of a ferrofluid Taking into Account Magnitophoresis and Particle Interaction","authors":"O. Lavrova, V. Polevikov","doi":"10.3846/mma.2022.14660","DOIUrl":"https://doi.org/10.3846/mma.2022.14660","url":null,"abstract":"Shielding properties of a cylindrical thick-walled ferrofluid layer that protects against externally applied uniform magnetic fields are numerically investigated. We take into account the diffusion of magnetic nanoparticles in the ferrofluid with magnetic dipole-dipole, steric and hydrodynamic interactions between particles. Permeability of the ferrofluid is considered to be dependent on the magnetic-field strength and the particle concentration. A combined method of finite differences and boundary elements is applied to solve a nonlinear transmission problem of magnetostatics in the whole space, augmented by nonlinear algebraic equations based on the mass transfer equation for magnetic nanoparticles in ferrofluids. Numerical experiments revealed that the diffusion of particles has negligible influence on the shielding properties at weak and strong intensities of the applied magnetic field when comparing with the results of computations for a uniform particle distribution.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73608830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Balčiūnas, V. Garbaliauskienė, Violeta Lukšienė, R. Macaitienė, Audronė Rimkevičienė
Let H(D) be the space of analytic functions on the strip ... In this paper, it is proved that there exists a closed non-empty set ...such that every collection of the functions ... is approximated by discrete shifts .., of Hurwitz zeta-functions with arbitrary parameters ...
{"title":"Joint discrete Approximation of analytic Functions by Hurwitz zeta-Functions","authors":"A. Balčiūnas, V. Garbaliauskienė, Violeta Lukšienė, R. Macaitienė, Audronė Rimkevičienė","doi":"10.3846/mma.2022.15068","DOIUrl":"https://doi.org/10.3846/mma.2022.15068","url":null,"abstract":"Let H(D) be the space of analytic functions on the strip ... In this paper, it is proved that there exists a closed non-empty set ...such that every collection of the functions ... is approximated by discrete shifts .., of Hurwitz zeta-functions with arbitrary parameters ...","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75625366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Jasas, A. Laurinčikas, M. Stoncelis, D. Šiaučiūnas
In the paper, an universality theorem of discrete type on the approximation of analytic functions by shifts of a special absolutely convergent Dirichlet series is obtained. These series is close in a certain sense to the periodic zeta-function and depends on a parameter.
{"title":"Discrete Universality of absolutely convergent Dirichlet Series","authors":"M. Jasas, A. Laurinčikas, M. Stoncelis, D. Šiaučiūnas","doi":"10.3846/mma.2022.15069","DOIUrl":"https://doi.org/10.3846/mma.2022.15069","url":null,"abstract":"In the paper, an universality theorem of discrete type on the approximation of analytic functions by shifts of a special absolutely convergent Dirichlet series is obtained. These series is close in a certain sense to the periodic zeta-function and depends on a parameter.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82164445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An investigation into the representation of integrals involving the product of the logarithm and the arctan functions, reducing to log-tangent integrals, will be undertaken in this paper. We will show that in many cases these integrals take an explicit form involving the Riemann zeta function, the Dirichlet eta function, Dirichlet lambda function and many other special functions. Some examples illustrating the theorems will be detailed.
{"title":"Evaluating Log-Tangent integrals via Euler sums","authors":"A. Sofo","doi":"10.3846/mma.2022.13100","DOIUrl":"https://doi.org/10.3846/mma.2022.13100","url":null,"abstract":"An investigation into the representation of integrals involving the product of the logarithm and the arctan functions, reducing to log-tangent integrals, will be undertaken in this paper. We will show that in many cases these integrals take an explicit form involving the Riemann zeta function, the Dirichlet eta function, Dirichlet lambda function and many other special functions. Some examples illustrating the theorems will be detailed.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75941079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this paper, we investigate the influence of two types of isolation on malware propagation within a computer network. Model 1 proposes the network quarantine strategy, where infected computers are fully disconnected from the network. As for model 2, the control strategy is the anti-virus software quarantine, where infected files in a computer are contained in an isolation folder. Both models consider the aspect of heterogeneous immunity, that is, weak and strong immunization of computers in a network. Analytical examinations produced a virus-free equilibrium and an endemic equilibrium for each model. It has been observed that the quarantine reproduction number R q plays an essential role in the existence and stability of the equilibrium points. Furthermore, numerical simulations are accomplished to substantiate the qualitative results. Finally, a sensitivity analysis is executed to specify the dominant parameters on R q . It is found that the performance of network quarantine is better than anti-virus software quarantine in controlling malware propagation.
{"title":"The Impact of Quarantine Strategies on Malware dynamics in a Network with Heterogeneous Immunity","authors":"Salma M. Al-Tuwairqi, Walaa S. Bahashwan","doi":"10.3846/mma.2022.14391","DOIUrl":"https://doi.org/10.3846/mma.2022.14391","url":null,"abstract":". In this paper, we investigate the influence of two types of isolation on malware propagation within a computer network. Model 1 proposes the network quarantine strategy, where infected computers are fully disconnected from the network. As for model 2, the control strategy is the anti-virus software quarantine, where infected files in a computer are contained in an isolation folder. Both models consider the aspect of heterogeneous immunity, that is, weak and strong immunization of computers in a network. Analytical examinations produced a virus-free equilibrium and an endemic equilibrium for each model. It has been observed that the quarantine reproduction number R q plays an essential role in the existence and stability of the equilibrium points. Furthermore, numerical simulations are accomplished to substantiate the qualitative results. Finally, a sensitivity analysis is executed to specify the dominant parameters on R q . It is found that the performance of network quarantine is better than anti-virus software quarantine in controlling malware propagation.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90904954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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