A. Halilu, M. Y. Waziri, A. Abdullahi, A. Majumder
A hybrid derivative-free double step length technique is proposed in this work in order to enhance the numerical results and convergence properties of the double direction and step length scheme. This is accomplished by combining a Picard-Mann hybrid iterative method proposed by Khan [Fix Point Theory and Applications, pp. 1-10, vol.69 (2013)] with the double step length approach. A derivative line search is employed in order to compute the two step lengths. Furthermore, a suitable acceleration parameter is developed to approximate the Jacobian matrix. Under some mild conditions, the proposed method is shown to converge globally. The numerical experiment presented in this paper illustrates the efficiency of the proposed method over some existing methods.
{"title":"On the Hybridization of the Double Step Length Method for Solving System of Nonlinear Equations","authors":"A. Halilu, M. Y. Waziri, A. Abdullahi, A. Majumder","doi":"10.47836/mjms.16.2.10","DOIUrl":"https://doi.org/10.47836/mjms.16.2.10","url":null,"abstract":"A hybrid derivative-free double step length technique is proposed in this work in order to enhance the numerical results and convergence properties of the double direction and step length scheme. This is accomplished by combining a Picard-Mann hybrid iterative method proposed by Khan [Fix Point Theory and Applications, pp. 1-10, vol.69 (2013)] with the double step length approach. A derivative line search is employed in order to compute the two step lengths. Furthermore, a suitable acceleration parameter is developed to approximate the Jacobian matrix. Under some mild conditions, the proposed method is shown to converge globally. The numerical experiment presented in this paper illustrates the efficiency of the proposed method over some existing methods.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42202014","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}
The primary objective of this paper is to develop the Refinement of Successive Over-Relaxation (RSOR) method based on a three-point linear rational finite difference-quadrature discretization scheme for the numerical solution of second-order linear Fredholm integro-differential equation (FIDE). Besides, to illuminate the superior performance of the proposed method, some numerical examples are presented and solved by implementing three approaches which are the Gauss-Seidel (GS), the Successive Over-Relaxation (SOR) and the RSOR methods. Lastly, through the comparison of the results, it is verified that the RSOR method is more effective than the other two methods, especially when considering the aspects of the number of iterations and running time.
{"title":"Refinement of SOR Iterative Method for the Linear Rational Finite Difference Solution of Second-Order Fredholm Integro-Differential Equations","authors":"M. M. Xu, J. Sulaiman, L. H. Ali","doi":"10.47836/mjms.16.1.09","DOIUrl":"https://doi.org/10.47836/mjms.16.1.09","url":null,"abstract":"The primary objective of this paper is to develop the Refinement of Successive Over-Relaxation (RSOR) method based on a three-point linear rational finite difference-quadrature discretization scheme for the numerical solution of second-order linear Fredholm integro-differential equation (FIDE). Besides, to illuminate the superior performance of the proposed method, some numerical examples are presented and solved by implementing three approaches which are the Gauss-Seidel (GS), the Successive Over-Relaxation (SOR) and the RSOR methods. Lastly, through the comparison of the results, it is verified that the RSOR method is more effective than the other two methods, especially when considering the aspects of the number of iterations and running time.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46354106","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}
In this paper, non-classical numerical schemes are proposed for the approximation of Cauchy type oscillatory and strongly singular integrals in complex plane. The schemes are developed by incorporating classical quadrature rule meant for the Cauchy type complex singular integrals over a line segment in complex plane with a quasi exact quadrature method meant for the numerical integration of complex definite integrals with an oscillatory weight function. The error bounds are established and the schemes are numerically validated using a set of standard test integrals. Numerical results show that these schemes are efficient.
{"title":"Non-Classical Quadrature Schemes for the Approximation of Cauchy Type\u0000Oscillatory and Singular Integrals in Complex Plane","authors":"S. A. K, Hota M. K., Mohanty P. K.","doi":"10.47836/mjms.16.1.02","DOIUrl":"https://doi.org/10.47836/mjms.16.1.02","url":null,"abstract":"In this paper, non-classical numerical schemes are proposed for the approximation of Cauchy type oscillatory and strongly singular integrals in complex plane. The schemes are developed by incorporating classical quadrature rule meant for the Cauchy type complex singular integrals over a line segment in complex plane with a quasi exact quadrature method meant for the numerical integration of complex definite integrals with an oscillatory weight function. The error bounds are established and the schemes are numerically validated using a set of standard test integrals. Numerical results show that these schemes are efficient.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47100258","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}
Aloev R. D., Eshkuvatov Z., Khudoyberganov M. U., Nematova D. E.
In this paper, we propose the difference splitting scheme for a mixed problem posed for n -dimensional symmetric t-hyperbolic systems. We construct the difference splitting scheme for the numerical calculation of stable solutions for this system. To build a difference scheme, a multidimensional problem is split into one-dimensional ones and solved for each direction. A discrete analogue of the Lyapunov’s function is constructed for the numerical verification of stability solutions for the considered problem. A priori estimate is obtained for the discrete analogue of the Lyapunov’s function. This estimate allows us to assert the exponential stability of the numerical solution. A theorem on the exponential stability solution of the boundary value problem for linear hyperbolic system was proved. These stability theorems give us the opportunity to prove the convergence of the numerical solution.
{"title":"The Difference Splitting Scheme for n-Dimensional Hyperbolic Systems","authors":"Aloev R. D., Eshkuvatov Z., Khudoyberganov M. U., Nematova D. E.","doi":"10.47836/mjms.16.1.01","DOIUrl":"https://doi.org/10.47836/mjms.16.1.01","url":null,"abstract":"In this paper, we propose the difference splitting scheme for a mixed problem posed for n -dimensional symmetric t-hyperbolic systems. We construct the difference splitting scheme for the numerical calculation of stable solutions for this system. To build a difference scheme, a multidimensional problem is split into one-dimensional ones and solved for each direction. A discrete analogue of the Lyapunov’s function is constructed for the numerical verification of stability solutions for the considered problem. A priori estimate is obtained for the discrete analogue of the Lyapunov’s function. This estimate allows us to assert the exponential stability of the numerical solution. A theorem on the exponential stability solution of the boundary value problem for linear hyperbolic system was proved. These stability theorems give us the opportunity to prove the convergence of the numerical solution.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47394764","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}
Z. Eshkuvatov, S. Ismail, Husnida Mamatova, D. S. Viscarra, R. Aloev
This paper considers systems of linear Fredholm-Volterra integral equations using a modified homotopy analysis method (MHAM) and the Gauss-Legendre quadrature formula (GLQF) to find approximate solutions. Standard homotopy analysis method (HAM), MHAM, and optimal homotopy asymptotic method (OHAM) are compared for the same number of iterations. It is noted from the chosen examples that MHAM with GLQF is comparable with standard HAM and OHAM. In all cases, MHAM with GLQF approaches exact solutions, where residual rapidly converges to zero when the number of iterations and quadrature nodes increases. The HAM developed in this paper is better than the HAM developed by Shidfar & Molabahrami in "Solving a system of integral equations by an analytic method".
{"title":"Modified HAM for solving linear system of Fredholm-Volterra Integral Equations","authors":"Z. Eshkuvatov, S. Ismail, Husnida Mamatova, D. S. Viscarra, R. Aloev","doi":"10.47836/mjms.16.1.08","DOIUrl":"https://doi.org/10.47836/mjms.16.1.08","url":null,"abstract":"This paper considers systems of linear Fredholm-Volterra integral equations using a modified homotopy analysis method (MHAM) and the Gauss-Legendre quadrature formula (GLQF) to find approximate solutions. Standard homotopy analysis method (HAM), MHAM, and optimal homotopy asymptotic method (OHAM) are compared for the same number of iterations. It is noted from the chosen examples that MHAM with GLQF is comparable with standard HAM and OHAM. In all cases, MHAM with GLQF approaches exact solutions, where residual rapidly converges to zero when the number of iterations and quadrature nodes increases. The HAM developed in this paper is better than the HAM developed by Shidfar & Molabahrami in \"Solving a system of integral equations by an analytic method\".","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"12 8","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41244643","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}
This paper presents a new construction of C1 cubic trigonometric spline interpolation. Instead of repositioning control points, a shape parameter is introduced in the spline to control the shape and behaviour of the curves. The built basis functions fulfil all the geometric properties of the standard cubic Bezier curve, and the proof is included in this paper. Then, the interpolation of the spline is illustrated using suitable parameter values. Every curve segment comprises four successive control points with a cubic trigonometric spline that carries out all the curve properties. The result showed effective approximation since the developed C1 cubic trigonometric spline produced a smooth and pleasant interpolating curve while preserving the positive data features. The flexibility of the developed spline is compared with the other two existing works: b-spline and bezier-like curves. The analysis shows that the proposed spline gives greater flexibility since it has a broader parameter value range. Therefore, this helps the spline interpolation build opened and closed curves, as incorporated in the paper.Munir, N. A. A. A
{"title":"C1 Cubic Trigonometric Spline with a Shape Parameter for Positive Shape Preservation","authors":"N. A. A. Munir, N. A. Hadi, M. Nasir","doi":"10.47836/mjms.16.1.05","DOIUrl":"https://doi.org/10.47836/mjms.16.1.05","url":null,"abstract":"This paper presents a new construction of C1 cubic trigonometric spline interpolation. Instead of repositioning control points, a shape parameter is introduced in the spline to control the shape and behaviour of the curves. The built basis functions fulfil all the geometric properties of the standard cubic Bezier curve, and the proof is included in this paper. Then, the interpolation of the spline is illustrated using suitable parameter values. Every curve segment comprises four successive control points with a cubic trigonometric spline that carries out all the curve properties. The result showed effective approximation since the developed C1 cubic trigonometric spline produced a smooth and pleasant interpolating curve while preserving the positive data features. The flexibility of the developed spline is compared with the other two existing works: b-spline and bezier-like curves. The analysis shows that the proposed spline gives greater flexibility since it has a broader parameter value range. Therefore, this helps the spline interpolation build opened and closed curves, as incorporated in the paper.Munir, N. A. A. A","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47098829","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}
R. Osman, Z. Hilmi, N. Ramli, N. Abdullah, N. M. F. H. N. B. Alam,
This paper discusses the images and metaphors of mathematics held by university students through their experiences of learning mathematics and the application of mathematical knowledge in real life. The study involved two hundred and four university students selected using purposive sampling and data was obtained through a question form shared online. The analysis was based on descriptive statistics, namely comparing percentages among the responses, since the measurement level of the data collected was either categorical or ordinal and there was no continuous data collected. The findings indicate that images and metaphors related to mathematics held by university students focused more on physical aspects rather than non-physical. Thus, the lack of understanding and imbalance in mathematics learning involving metaphysical domains needs to be observed in detail.
{"title":"Images and Metaphors of Mathematics Among University Students","authors":"R. Osman, Z. Hilmi, N. Ramli, N. Abdullah, N. M. F. H. N. B. Alam,","doi":"10.47836/mjms.16.1.06","DOIUrl":"https://doi.org/10.47836/mjms.16.1.06","url":null,"abstract":"This paper discusses the images and metaphors of mathematics held by university students through their experiences of learning mathematics and the application of mathematical knowledge in real life. The study involved two hundred and four university students selected using purposive sampling and data was obtained through a question form shared online. The analysis was based on descriptive statistics, namely comparing percentages among the responses, since the measurement level of the data collected was either categorical or ordinal and there was no continuous data collected. The findings indicate that images and metaphors related to mathematics held by university students focused more on physical aspects rather than non-physical. Thus, the lack of understanding and imbalance in mathematics learning involving metaphysical domains needs to be observed in detail.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49147413","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}
In this paper, a special class of rings for which an element a in R, satisfying the additional property an=an−1+an−1, for an integer n>1 is introduced and several results and examples related to this special class of rings is presented.
{"title":"A Special Class of Rings","authors":"T. Nagaiah, M. R. Valluri","doi":"10.47836/mjms.16.1.11","DOIUrl":"https://doi.org/10.47836/mjms.16.1.11","url":null,"abstract":"In this paper, a special class of rings for which an element a in R, satisfying the additional property an=an−1+an−1, for an integer n>1 is introduced and several results and examples related to this special class of rings is presented.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49639954","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}
For a graph G, we define a total k-labeling ϕ as a combination of an edge labeling ϕe(x) → {1, 2, . . . , ke} and a vertex labeling ϕv(x) → {0, 2, . . . , 2kv}, such that ϕ(x) = ϕv(x) if x ∈ V (G) and ϕ(x) = ϕe(x) if x ∈ E(G), where k = max {ke, 2kv}. The total k-labeling ϕ is called an edge irregular reflexive k-labeling of G, if for every two edges xy, x0y0of G, one has wt(xy) 6=wt(x0y0), where wt(xy) = ϕv(x) + ϕe(xy) + ϕv(y). The smallest value of k for which such labeling exists is called a reflexive edge strength of G. In this paper, we study the edge irregular reflexive labeling on plane graphs and determine its reflexive edge strength.
{"title":"Edge Irregular Reflexive Labeling for Some Classes of Plane Graphs","authors":"Yoong K. K., Hasni R., Lau G. C., Irfan M.","doi":"10.47836/mjms.16.1.03","DOIUrl":"https://doi.org/10.47836/mjms.16.1.03","url":null,"abstract":"For a graph G, we define a total k-labeling ϕ as a combination of an edge labeling ϕe(x) →\u0000{1, 2, . . . , ke} and a vertex labeling ϕv(x) → {0, 2, . . . , 2kv}, such that ϕ(x) = ϕv(x) if x ∈\u0000V (G) and ϕ(x) = ϕe(x) if x ∈ E(G), where k = max {ke, 2kv}. The total k-labeling ϕ is called\u0000an edge irregular reflexive k-labeling of G, if for every two edges xy, x0y0of G, one has wt(xy) 6=wt(x0y0), where wt(xy) = ϕv(x) + ϕe(xy) + ϕv(y). The smallest value of k for which such labeling exists is called a reflexive edge strength of G. In this paper, we study the edge irregular reflexive labeling on plane graphs and determine its reflexive edge strength.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43582648","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}
In this paper, the transmission of HIV-HBV co-infection is carried out. The individuals who are infected with both diseases HIV and HBV simultaneously, are said to be HIV-HBV co-infected. These infected individuals have high risk of liver failure. It is the main cause for serious liver complications like cirrhosis and liver cancer at younger age. A deterministic model is considered with liquor habit in men and vaccination to new-borns and carrier mother. Carrier class results in the vertical transmission. In this paper, the transmission dynamics of the model is analyzed. The total population is divided in to twenty eight class viz. Susceptible, HBV Vaccinated, HBV-infected female, HBV-carrier female, HBV infected alcoholic male, HBV carrier alcoholic male, HBV infected non-alcoholic male, HBV carrier non-alcoholic male, HBV recovered class, pre-AIDS female, AIDS female, pre-AIDS-HBV co-infected female, AIDS-HBV co-infected female, pre-AIDS-HBV carrier female, AIDS-HBV carrier female, pre-AIDS alcoholic male, AIDS alcoholic male, pre-AIDS non-alcoholic male, AIDS non-alcoholic male, pre-AIDS-HBV co-infected alcoholic male, pre-AIDS-HBV co-infected non-alcoholic male, pre-AIDS-HBV carrier alcoholic male, pre-AIDS-HBV carrier non-alcoholic male, AIDS-HBV co-infected alcoholic male, AIDS-HBV co-infected non-alcoholic male, AIDS-HBV carrier non-alcoholic male, HIV infected -HBV recovered classes. The basic reproduction numbers for HIV, for HBV and for HIV-HBV are found using next generation matrix. Local and global stability of HIV-HBV disease free equilibrium is worked out. Model is validated with the numerical simulation.
{"title":"Vertical Transmission of HIV-HBV Co-infection with Liquor Habit and Vaccination","authors":"N. H. Shah, Z. A. Patel, B. M. Yeolekar","doi":"10.47836/mjms.16.1.10","DOIUrl":"https://doi.org/10.47836/mjms.16.1.10","url":null,"abstract":"In this paper, the transmission of HIV-HBV co-infection is carried out. The individuals who are infected with both diseases HIV and HBV simultaneously, are said to be HIV-HBV co-infected. These infected individuals have high risk of liver failure. It is the main cause for serious liver complications like cirrhosis and liver cancer at younger age. A deterministic model is considered with liquor habit in men and vaccination to new-borns and carrier mother. Carrier class results in the vertical transmission. In this paper, the transmission dynamics of the model is analyzed. The total population is divided in to twenty eight class viz. Susceptible, HBV Vaccinated, HBV-infected female, HBV-carrier female, HBV infected alcoholic male, HBV carrier alcoholic male, HBV infected non-alcoholic male, HBV carrier non-alcoholic male, HBV recovered class, pre-AIDS female, AIDS female, pre-AIDS-HBV co-infected female, AIDS-HBV co-infected female, pre-AIDS-HBV carrier female, AIDS-HBV carrier female, pre-AIDS alcoholic male, AIDS alcoholic male, pre-AIDS non-alcoholic male, AIDS non-alcoholic male, pre-AIDS-HBV co-infected alcoholic male, pre-AIDS-HBV co-infected non-alcoholic male, pre-AIDS-HBV carrier alcoholic male, pre-AIDS-HBV carrier non-alcoholic male, AIDS-HBV co-infected alcoholic male, AIDS-HBV co-infected non-alcoholic male, AIDS-HBV carrier non-alcoholic male, HIV infected -HBV recovered classes. The basic reproduction numbers for HIV, for HBV and for HIV-HBV are found using next generation matrix. Local and global stability of HIV-HBV disease free equilibrium is worked out. Model is validated with the numerical simulation.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41867671","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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