Pub Date : 2021-12-31DOI: 10.24203/ajfam.v9i3.6805
A. Filiz
In this paper, we study the uniformly convergent method on equidistant meshes for the convection-diffusion problem of type; where the formal adjoint operator of L. Lu=-εu''+bu'+c u=f(x), u(0)=0, u(1)=0 At the end of the this paper we will generate the scheme; -e^(ρ_i )/(e^(ρ_i )+1) U_(i-1)+U_i-1/(e^(ρ_i )+1) U_(i+1)=(f_i-c_i U_i ) h/b ((e^(ρ_i )-1)/(e^(ρ_i )+1))
{"title":"Analytical Construction of Uniformly Convergent Method for Convection Diffusion Problem","authors":"A. Filiz","doi":"10.24203/ajfam.v9i3.6805","DOIUrl":"https://doi.org/10.24203/ajfam.v9i3.6805","url":null,"abstract":"In this paper, we study the uniformly convergent method on equidistant meshes for the convection-diffusion problem of type;\u0000where the formal adjoint operator of L.\u0000Lu=-εu''+bu'+c u=f(x), u(0)=0, u(1)=0\u0000At the end of the this paper we will generate the scheme;\u0000-e^(ρ_i )/(e^(ρ_i )+1) U_(i-1)+U_i-1/(e^(ρ_i )+1) U_(i+1)=(f_i-c_i U_i ) h/b ((e^(ρ_i )-1)/(e^(ρ_i )+1))","PeriodicalId":446683,"journal":{"name":"Asian Journal of Fuzzy and Applied Mathematics","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114525598","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 : 2019-04-20DOI: 10.24203/AJFAM.V7I2.5736
R. Rasuli
In this study, by using t-norms, fuzzy equivalence relation, fuzzy congrunce relation on group G, fuzzy relation of subgroup H of group G, fuzzy normal subgroups of fuzzy subgroups, direct product of fuzzy subgroups(normal fuzzy subgroups) are introduced and some the their properties will be discussed. Next by using group homomorphisms, the image and pree image of them will be investigated.
{"title":"Fuzzy Equivalence Relation, Fuzzy Congrunce Relation and Fuzzy Normal Subgroups on Group G Over T-Norms","authors":"R. Rasuli","doi":"10.24203/AJFAM.V7I2.5736","DOIUrl":"https://doi.org/10.24203/AJFAM.V7I2.5736","url":null,"abstract":"In this study, by using t-norms, fuzzy equivalence relation, fuzzy congrunce relation on group G, fuzzy relation of subgroup H of group G, fuzzy normal subgroups of fuzzy subgroups, direct product of fuzzy subgroups(normal fuzzy subgroups) are introduced and some the their properties will be discussed. Next by using group homomorphisms, the image and pree image of them will be investigated.","PeriodicalId":446683,"journal":{"name":"Asian Journal of Fuzzy and Applied Mathematics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125323003","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 : 2019-02-17DOI: 10.24203/AJFAM.V7I1.5619
B. Kalimbetov
In this paper we consider initial problem for an ordinary differential equation of fractional order with a small parameter for the derivative. S.A. Lomov regularization method is used to construct an asymptotic approximate solution of the problem with accuracy up to any power of a small parameter. Using the computer mathematics system (CMS) Maple, a symbolic solution of the original problem is obtained, and solution schedules are constructed, depending on the initial data and various values of the small parameter. It is shown that the asymptotic solution presented in the form of a specific convergent series and the solution represented by the CMS Maple coincides with the exact solution of the original problem.Â
{"title":"Scalar Singularly Perturbed Cauchy Problem for a Differential Equation of Fractional Order","authors":"B. Kalimbetov","doi":"10.24203/AJFAM.V7I1.5619","DOIUrl":"https://doi.org/10.24203/AJFAM.V7I1.5619","url":null,"abstract":"In this paper we consider initial problem for an ordinary differential equation of fractional order with a small parameter for the derivative. S.A. Lomov regularization method is used to construct an asymptotic approximate solution of the problem with accuracy up to any power of a small parameter. Using the computer mathematics system (CMS) Maple, a symbolic solution of the original problem is obtained, and solution schedules are constructed, depending on the initial data and various values of the small parameter. It is shown that the asymptotic solution presented in the form of a specific convergent series and the solution represented by the CMS Maple coincides with the exact solution of the original problem. ","PeriodicalId":446683,"journal":{"name":"Asian Journal of Fuzzy and Applied Mathematics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123433441","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 : 2019-02-17DOI: 10.24203/AJFAM.V7I1.5620
B. Kalimbetov
As is known, many problems of electronics, nuclear physics, optics and astrophysics, etc. are described by the Abel integral equation of the first kind. In this paper we consider the nonlinear generalized Abel equation and show that its solution can be represented as an integral of a power function. It is shown that the constructed analytical solution and the symbolic solution obtained by means of the computer mathematics system Maple coincides, and their planar and spatial graphs are presented.
{"title":"About Solution of the Nonlinear Generalized Abel Integral Equation","authors":"B. Kalimbetov","doi":"10.24203/AJFAM.V7I1.5620","DOIUrl":"https://doi.org/10.24203/AJFAM.V7I1.5620","url":null,"abstract":"As is known, many problems of electronics, nuclear physics, optics and astrophysics, etc. are described by the Abel integral equation of the first kind. In this paper we consider the nonlinear generalized Abel equation and show that its solution can be represented as an integral of a power function. It is shown that the constructed analytical solution and the symbolic solution obtained by means of the computer mathematics system Maple coincides, and their planar and spatial graphs are presented.","PeriodicalId":446683,"journal":{"name":"Asian Journal of Fuzzy and Applied Mathematics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126710819","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 : 2019-02-17DOI: 10.24203/ajfam.v7i1.5668
Ayse Metin Karakaş, S. Çalik
In this paper, we firstly give basic definitions and theorems for order statistics. Later, we show that r. probability function of order statistics from discrete uniform distribution can be obtained in another form.
{"title":"Probability Functions of Order Statistics from Discrete Uniform Distribution","authors":"Ayse Metin Karakaş, S. Çalik","doi":"10.24203/ajfam.v7i1.5668","DOIUrl":"https://doi.org/10.24203/ajfam.v7i1.5668","url":null,"abstract":"In this paper, we firstly give basic definitions and theorems for order statistics. Later, we show that r. probability function of order statistics from discrete uniform distribution can be obtained in another form.","PeriodicalId":446683,"journal":{"name":"Asian Journal of Fuzzy and Applied Mathematics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129267165","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 : 2018-12-15DOI: 10.24203/ajfam.v6i3.5600
B. Kalimbetov
In this paper we consider an initial problem for systems of differential equations of fractional order with a small parameter for the derivative. Regularization problem is produced, and algorithm for normal and unique solubility of general iterative systems of differential equations with partial derivatives is given.Â
{"title":"On the Question of Asymptotic Integration of Singularly Perturbed Fractional-Order Problems","authors":"B. Kalimbetov","doi":"10.24203/ajfam.v6i3.5600","DOIUrl":"https://doi.org/10.24203/ajfam.v6i3.5600","url":null,"abstract":"In this paper we consider an initial problem for systems of differential equations of fractional order with a small parameter for the derivative. Regularization problem is produced, and algorithm for normal and unique solubility of general iterative systems of differential equations with partial derivatives is given. ","PeriodicalId":446683,"journal":{"name":"Asian Journal of Fuzzy and Applied Mathematics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117107571","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 : 2018-12-15DOI: 10.24203/AJFAM.V6I3.5598
B. Kalimbetov, R. Turgunbaev
The paper is devoted to construction of an asymptotic solution of a weakly nonlinear singularly perturbed differential system of fractional order. To construct the asymptotic solution we use ideas of normal differential forms method of V.F. Safonov. In the environment of the computer mathematical system Maple, approximate solutions are calculated, and corresponding solution schedules for various values of a small parameter are constructed.
{"title":"Regularization Method for Nonlinear Singularly Perturbed Systems of Fractional Order","authors":"B. Kalimbetov, R. Turgunbaev","doi":"10.24203/AJFAM.V6I3.5598","DOIUrl":"https://doi.org/10.24203/AJFAM.V6I3.5598","url":null,"abstract":"The paper is devoted to construction of an asymptotic solution of a weakly nonlinear singularly perturbed differential system of fractional order. To construct the asymptotic solution we use ideas of normal differential forms method of V.F. Safonov. In the environment of the computer mathematical system Maple, approximate solutions are calculated, and corresponding solution schedules for various values of a small parameter are constructed.","PeriodicalId":446683,"journal":{"name":"Asian Journal of Fuzzy and Applied Mathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133399549","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 : 2018-10-19DOI: 10.24203/ajfam.v6i2.5510
S. N. Huseen, Haider A. Mkharrib
In this paper, new powerful modification of homotopy analysis technique (NMHAM) was submitted to create an approximate solution of nonhomogeneous nonlinear ordinary and partial differential equations. The NMHAM is a combination of the new technique of homotopy analysis method(NHAM) [4] and the new technique of homotopy analysis method(nHAM) [7].Three illustrative examples are employed to illustrate the accuracy and computational proficiency of this approach. The outcomes uncover that the NMHAM is more accurate than the NHAM and nHAM.
{"title":"On a New Modification of Homotopy Analysis Method for Solving Nonlinear Nonhomogeneous Differential Equations","authors":"S. N. Huseen, Haider A. Mkharrib","doi":"10.24203/ajfam.v6i2.5510","DOIUrl":"https://doi.org/10.24203/ajfam.v6i2.5510","url":null,"abstract":"In this paper, new powerful modification of homotopy analysis technique (NMHAM) was submitted to create an approximate solution of nonhomogeneous nonlinear ordinary and partial differential equations. The NMHAM is a combination of the new technique of homotopy analysis method(NHAM) [4] and the new technique of homotopy analysis method(nHAM) [7].Three illustrative examples are employed to illustrate the accuracy and computational proficiency of this approach. The outcomes uncover that the NMHAM is more accurate than the NHAM and nHAM.","PeriodicalId":446683,"journal":{"name":"Asian Journal of Fuzzy and Applied Mathematics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130448738","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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