This research article presents a novel approach called the delta-power transformation, which introduces a new class of lifetime distributions. The article discusses the key features of one member from this family, which exhibits a hazard function with a distinctive shape resembling a J, reverse-J, constant, or monotonically increasing. The researchers delve into the statistical characteristics of this distribution and utilize the maximum likelihood estimation (MLE) approach to gauge its parameters. They conduct a simulation experiment to evaluate the precision of the estimation process, finding that biases and mean square errors diminish with larger sample sizes, even in cases involving small samples. Moreover, the study show-cases the practical utility of the suggested distribution through an examination of two real-world datasets. Evaluation criteria for model selection and goodness-of-fit test statistics indicate that the proposed model surpasses certain existing models in performance.
{"title":"Delta Power Transformation: A New Family of Probability Distributions","authors":"L. Sapkota, Pankaj Kumar, Vijay Kumar","doi":"10.3126/jnms.v7i1.67488","DOIUrl":"https://doi.org/10.3126/jnms.v7i1.67488","url":null,"abstract":"This research article presents a novel approach called the delta-power transformation, which introduces a new class of lifetime distributions. The article discusses the key features of one member from this family, which exhibits a hazard function with a distinctive shape resembling a J, reverse-J, constant, or monotonically increasing. The researchers delve into the statistical characteristics of this distribution and utilize the maximum likelihood estimation (MLE) approach to gauge its parameters. They conduct a simulation experiment to evaluate the precision of the estimation process, finding that biases and mean square errors diminish with larger sample sizes, even in cases involving small samples. Moreover, the study show-cases the practical utility of the suggested distribution through an examination of two real-world datasets. Evaluation criteria for model selection and goodness-of-fit test statistics indicate that the proposed model surpasses certain existing models in performance.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":" 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141677301","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}
Production of bi-layer tablets involves the concept of tandem queue. Tandem queue is a series of queues in which the output of one queue becomes the input to the next queue. In this paper, two tandem queues are employed. Each queue has heterogeneous mean arrival time and service time. These two queues merge into one finite capacity queue in the production process of the bi-layer tablets. The study investigates various performance measures of the queueing model. Mathematical models and simulations are utilized to evaluate system performance under different scenarios.
{"title":"Tandem Queue and Its Applications in the Production of Bi-layer Tablets","authors":"Ritu Basnet Thapa, Sushil Ghimire, Ram Prasad Ghimire","doi":"10.3126/jnms.v7i1.67491","DOIUrl":"https://doi.org/10.3126/jnms.v7i1.67491","url":null,"abstract":"Production of bi-layer tablets involves the concept of tandem queue. Tandem queue is a series of queues in which the output of one queue becomes the input to the next queue. In this paper, two tandem queues are employed. Each queue has heterogeneous mean arrival time and service time. These two queues merge into one finite capacity queue in the production process of the bi-layer tablets. The study investigates various performance measures of the queueing model. Mathematical models and simulations are utilized to evaluate system performance under different scenarios.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":" 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141679279","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 article, we consider two algorithms, dimension and inversion pairs of rows-strict, used for the computation of Betti numbers of Springer varieties and then show that the sequences respectively generated by these algorithms are dual to each other, (except for λ = 1n where Ik = Dk) and that the sum Ik + Dk gives another sequence which is palindromic. We also show that for each row-strict tableau τ of shape λ = n − r, 1r (0 ≤ r ≤ n − 1), the dimension of the corresponding Springer varieties equals the cardinality of the union of the set of inversions and dimensions of τ. This research contributes to a deeper understanding of the rich combinatorial landscape of tableaux, opening up new avenues for further research.
在本文中，我们考虑了用于计算斯普林格变体的贝蒂数的两种算法，即行-严格的维数和反演对，然后证明了由这些算法分别生成的序列是对偶的（除了 λ = 1n 时 Ik = Dk），并且和 Ik + Dk 给出的另一个序列是回文序列。我们还证明，对于形状为 λ = n - r, 1r (0 ≤ r ≤ n - 1) 的每一个行严格表头 τ，相应 Springer varieties 的维数等于 τ 的反转集和维数的联合的万有引力。这项研究有助于加深对表头丰富组合景观的理解，为进一步研究开辟了新途径。
{"title":"On the Inversion and Dimension Pairs of Row-Strict Tableaux","authors":"Felemu Olasupo, Adetunji Patience","doi":"10.3126/jnms.v7i1.67485","DOIUrl":"https://doi.org/10.3126/jnms.v7i1.67485","url":null,"abstract":"In this article, we consider two algorithms, dimension and inversion pairs of rows-strict, used for the computation of Betti numbers of Springer varieties and then show that the sequences respectively generated by these algorithms are dual to each other, (except for λ = 1n where Ik = Dk) and that the sum Ik + Dk gives another sequence which is palindromic. We also show that for each row-strict tableau τ of shape λ = n − r, 1r (0 ≤ r ≤ n − 1), the dimension of the corresponding Springer varieties equals the cardinality of the union of the set of inversions and dimensions of τ. This research contributes to a deeper understanding of the rich combinatorial landscape of tableaux, opening up new avenues for further research.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":" 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141679802","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, we investigate and study various new notions of statistical convergence criteria of martingale sequences via deferred Ces`aro mean. We then establish several results concerning the relation among these beautiful and potentially useful concepts. Moreover, our proposed techniques contributed to finding several new approximation results of the Korovkin-type for martingale sequences over complete normed linear spaces. We also present some concrete examples to establish the stronger side of our results.
{"title":"On Certain Statistical Convergence Criteria for Martingale Sequences via Deferred Ces`aro Mean with Some Applications","authors":"Hemen Dutta, B. Jena, N. Pahari, S. K. Paikray","doi":"10.3126/jnms.v7i1.67486","DOIUrl":"https://doi.org/10.3126/jnms.v7i1.67486","url":null,"abstract":"In this paper, we investigate and study various new notions of statistical convergence criteria of martingale sequences via deferred Ces`aro mean. We then establish several results concerning the relation among these beautiful and potentially useful concepts. Moreover, our proposed techniques contributed to finding several new approximation results of the Korovkin-type for martingale sequences over complete normed linear spaces. We also present some concrete examples to establish the stronger side of our results.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":" 38","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141679117","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}
Jeevan Kafle, K. Adhikari, Eeshwar Prasad Poudel, Ramesh Raj Pant
Air pollution is one of the biggest problems in both developed and developing countries. Mathematical modeling is widely applied to assess how air pollutants impact on human and ecological health. In this paper, the fundamental behavior of the plumes along with stack height and the underlying assumptions of the Gaussian plume model were assessed. Additionally, the equation for advection and diffusion was also developed to analyze the pollutants concentration of brick kilns. Basically, the model considers the height, emission sources, eddy diffusivity, and wind profile as parameters by adopting the fundamental approaches of the model. Interestingly, the results revealed that when the stack height is reduced, pollutants are more prominent whereas when the stack height is increased, the pollutants are less prevalent along the x-axis. There is a close relationship between wind velocity and pollutants dispersion. The model illustrates that stronger winds tend to increase the dispersion of air pollutants; hence, areas with stronger winds typically have lower air pollution concentrations. The insights of this work will directly contribute to environmental sustainability by mitigating pollutants concentration, especially in the core urban areas. Additionally, the work is also applicable for the researcher and academia to select the optimal measurement techniques and ways forward for controlling the pollution level in the atmosphere.
空气污染是发达国家和发展中国家面临的最大问题之一。数学模型被广泛应用于评估空气污染物对人类和生态健康的影响。本文评估了烟羽的基本行为、烟囱高度和高斯烟羽模型的基本假设。此外，还建立了平流和扩散方程，以分析砖窑的污染物浓度。基本上，该模型采用模型的基本方法，将高度、排放源、涡流扩散率和风廓线作为参数。有趣的是，结果显示，当烟囱高度降低时，污染物更加突出，而当烟囱高度增加时，沿 x 轴的污染物则减少。风速与污染物扩散之间存在密切关系。该模型表明，风力越强，空气污染物的扩散量越大；因此，风力越强的地区空气污染浓度通常越低。这项工作的见解将通过降低污染物浓度，特别是城市核心区域的污染物浓度，直接促进环境的可持续发展。此外，这项工作也适用于研究人员和学术界选择最佳测量技术和控制大气污染水平的方法。
{"title":"Mathematical Modeling of Pollutants Dispersion in the Atmosphere","authors":"Jeevan Kafle, K. Adhikari, Eeshwar Prasad Poudel, Ramesh Raj Pant","doi":"10.3126/jnms.v7i1.67487","DOIUrl":"https://doi.org/10.3126/jnms.v7i1.67487","url":null,"abstract":"Air pollution is one of the biggest problems in both developed and developing countries. Mathematical modeling is widely applied to assess how air pollutants impact on human and ecological health. In this paper, the fundamental behavior of the plumes along with stack height and the underlying assumptions of the Gaussian plume model were assessed. Additionally, the equation for advection and diffusion was also developed to analyze the pollutants concentration of brick kilns. Basically, the model considers the height, emission sources, eddy diffusivity, and wind profile as parameters by adopting the fundamental approaches of the model. Interestingly, the results revealed that when the stack height is reduced, pollutants are more prominent whereas when the stack height is increased, the pollutants are less prevalent along the x-axis. There is a close relationship between wind velocity and pollutants dispersion. The model illustrates that stronger winds tend to increase the dispersion of air pollutants; hence, areas with stronger winds typically have lower air pollution concentrations. The insights of this work will directly contribute to environmental sustainability by mitigating pollutants concentration, especially in the core urban areas. Additionally, the work is also applicable for the researcher and academia to select the optimal measurement techniques and ways forward for controlling the pollution level in the atmosphere.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":" 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141678556","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 work, we incorporate the solution of Richards equation in infinite slope model to locate the potential landslide hazards area and prediction of landslide hazards induced by heavy rainfall, continuously precipitation and redistribution. Firstly, we modeled the Richards equation in cylindrical coordinate with axial symmetry and use Kirchhoff ’s transformation to linearize it. With Kirchhoff ’s transformation the nonlinear axi-symmetric model is transformed into the nonlinear parabolic equation. Because of its high non-linear properties, analytical solutions of Richards equation are rare and limited for particular cases with hardly reliable. To solve the equation numerically, different approximation techniques as FDM, FVM are used on the prescribed model. Since, the landslide hazards problems are accelerated by safety factor which are related to the forces that restrain the surface from failure and endow the surface to smash. Hence to evaluate the safety factor we use the infinite slope model characterized with moisture content, pressure head in variably saturated (unsaturated) soils. The attachment of Richards equation along with the infinite slope model in the expression of safety factor which helps to explore the surface failure condition for different soils for their different physical characteristic including precipitation, infiltration, redistribution and moisture content.
{"title":"Infiltration-Induced Landslide: An Application of Richards Equation","authors":"Ramesh Chandra Timsina","doi":"10.3126/jnms.v7i1.67490","DOIUrl":"https://doi.org/10.3126/jnms.v7i1.67490","url":null,"abstract":"In this work, we incorporate the solution of Richards equation in infinite slope model to locate the potential landslide hazards area and prediction of landslide hazards induced by heavy rainfall, continuously precipitation and redistribution. Firstly, we modeled the Richards equation in cylindrical coordinate with axial symmetry and use Kirchhoff ’s transformation to linearize it. With Kirchhoff ’s transformation the nonlinear axi-symmetric model is transformed into the nonlinear parabolic equation. Because of its high non-linear properties, analytical solutions of Richards equation are rare and limited for particular cases with hardly reliable. To solve the equation numerically, different approximation techniques as FDM, FVM are used on the prescribed model. Since, the landslide hazards problems are accelerated by safety factor which are related to the forces that restrain the surface from failure and endow the surface to smash. Hence to evaluate the safety factor we use the infinite slope model characterized with moisture content, pressure head in variably saturated (unsaturated) soils. The attachment of Richards equation along with the infinite slope model in the expression of safety factor which helps to explore the surface failure condition for different soils for their different physical characteristic including precipitation, infiltration, redistribution and moisture content.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":" 89","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141680281","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 study, we introduce the Cauchy modified inverse Gompertz distribution as a new probability model. Utilizing the modified inverse Gompertz distribution as its baseline distribution, this model blends the Cauchy family of distributions. Our aim is to utilize this model for lifetime data analysis. We have inferred formulas for some basic properties of the model. We have also included graphic representations of the hazard rate and probability density curves. We observed that the probability density function displays positive skewness, while the hazard rate function plot shows an increasing-decreasing pattern. We used the Cramer-Von Mises method, the least squares approach, and maximum likelihood estimation to estimate the model parameters. We employed several statistical criteria to validate our model, including the corrected Akaike’s, the Bayesian, the Hannan-Quinn, as well as Akaike’s information criterion. We also utilized Q-Q and P-P graphs for further confirmation. To assess goodness of fit, we used the Kolmogorov-Smirnov, Anderson-Darlin, and Cramer-von Mises tests. The empirical results of the study show that it gives a better fit to the real data set. All numerical computations were conducted using the R programming language.
{"title":"Model and Properties of Cauchy Modified Inverse Gompertz Distribution with Application to a Real Data Set","authors":"A. Chaudhary, Lal Babu Sah Telee","doi":"10.3126/jnms.v7i1.67483","DOIUrl":"https://doi.org/10.3126/jnms.v7i1.67483","url":null,"abstract":"In this study, we introduce the Cauchy modified inverse Gompertz distribution as a new probability model. Utilizing the modified inverse Gompertz distribution as its baseline distribution, this model blends the Cauchy family of distributions. Our aim is to utilize this model for lifetime data analysis. We have inferred formulas for some basic properties of the model. We have also included graphic representations of the hazard rate and probability density curves. We observed that the probability density function displays positive skewness, while the hazard rate function plot shows an increasing-decreasing pattern. We used the Cramer-Von Mises method, the least squares approach, and maximum likelihood estimation to estimate the model parameters. We employed several statistical criteria to validate our model, including the corrected Akaike’s, the Bayesian, the Hannan-Quinn, as well as Akaike’s information criterion. We also utilized Q-Q and P-P graphs for further confirmation. To assess goodness of fit, we used the Kolmogorov-Smirnov, Anderson-Darlin, and Cramer-von Mises tests. The empirical results of the study show that it gives a better fit to the real data set. All numerical computations were conducted using the R programming language.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":" 68","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141680108","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}
Dwarika Prasad Gautam, Ramesh Gautam, Khagendra Adhikari, A. Pokharel, K. N. Uprety
Increasing incidence of dengue fever has become an important health concern in recent years, especially in developing country like Nepal. To investigate patterns of transmission, this work uses a mathematical model for the dynamics of dengue outbreaks in the Rupandehi district in 2017. To validate the model biologically, we demonstrate the positivity and boundedness of solutions. Furthermore, we establish that for R0 < 1, the disease-free equilibrium is locally asymptotically stable, whereas for R0 > 1, a unique endemic equilibrium point exists. Sensitivity analysis showed that the parameters related to mosquitoes, in particular the mosquito death rate (µv) and mosquito biting rate in transmission rates (β1, β2, βv), have signifcant impact on R0. Therefore, implementing mosquito control activities followed by protection against mosquito bites are crucial strategies in effectively controlling dengue transmission.
{"title":"Transmission Dynamics of Dengue Disease in the Rupandehi District of Nepal","authors":"Dwarika Prasad Gautam, Ramesh Gautam, Khagendra Adhikari, A. Pokharel, K. N. Uprety","doi":"10.3126/jnms.v7i1.67586","DOIUrl":"https://doi.org/10.3126/jnms.v7i1.67586","url":null,"abstract":"Increasing incidence of dengue fever has become an important health concern in recent years, especially in developing country like Nepal. To investigate patterns of transmission, this work uses a mathematical model for the dynamics of dengue outbreaks in the Rupandehi district in 2017. To validate the model biologically, we demonstrate the positivity and boundedness of solutions. Furthermore, we establish that for R0 < 1, the disease-free equilibrium is locally asymptotically stable, whereas for R0 > 1, a unique endemic equilibrium point exists. Sensitivity analysis showed that the parameters related to mosquitoes, in particular the mosquito death rate (µv) and mosquito biting rate in transmission rates (β1, β2, βv), have signifcant impact on R0. Therefore, implementing mosquito control activities followed by protection against mosquito bites are crucial strategies in effectively controlling dengue transmission.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":" 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141677110","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}
Let G(α, β), A(α, β) and H(α, β), respectively, be the geometric mean, arithmetic mean and harmonic mean of α and β. In this paper, we prove that G(ψ′ (z), ψ′ (1/z)) ≥ π2/6, A(ψ′ (z), ψ′ (1/z)) ≥ π2/6 and H(ψ′ (z), ψ′ (1/z)) ≤ π2/6. This extends the previous results of Alzer and Jameson regarding the digamma function ψ. The mathematical tools used to prove the results include convexity, concavity and monotonicity properties of certain functions as well as the convolution theorem for Laplace transforms.
{"title":"Inequalities for Means Regarding the Trigamma Function","authors":"K. Nantomah, G. Abe-I-Kpeng, Sunday Sandow","doi":"10.3126/jnms.v6i2.63030","DOIUrl":"https://doi.org/10.3126/jnms.v6i2.63030","url":null,"abstract":"Let G(α, β), A(α, β) and H(α, β), respectively, be the geometric mean, arithmetic mean and harmonic mean of α and β. In this paper, we prove that G(ψ′ (z), ψ′ (1/z)) ≥ π2/6, A(ψ′ (z), ψ′ (1/z)) ≥ π2/6 and H(ψ′ (z), ψ′ (1/z)) ≤ π2/6. This extends the previous results of Alzer and Jameson regarding the digamma function ψ. The mathematical tools used to prove the results include convexity, concavity and monotonicity properties of certain functions as well as the convolution theorem for Laplace transforms.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"39 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140429420","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, we study error estimates in the maximum norm in the context of solving Poisson’s equation numerically when approximated the Five-Point Laplacian method using the discrete maximum principle. The primary objective is to assess the accuracy of this numerical approach in solving Poisson’s equation and to provide insights into the behavior of error estimates. We focus on the estimates of maximum norm of the discrete functions defined on a grid in a unit square as well as in a square of side s, and estimate errors measured in the maximum norm.
在本文中，我们研究了利用离散最大值原理近似五点拉普拉斯方法数值求解泊松方程时的最大值规范误差估计。主要目的是评估这种数值方法在求解泊松方程时的准确性，并深入了解误差估计的行为。我们重点研究了在单位正方形和边长为 s 的正方形网格上定义的离散函数的最大法的估计，并估计了以最大法测量的误差。
{"title":"Error Estimates in the Maximum Norm for the Solution of Poisson’s Equation Approximated by the Five-Point Laplacian Using the Discrete Maximum Principle","authors":"Ganesh Bahadur Basnet, Madhav Poudel, Resham Prasad Paudel","doi":"10.3126/jnms.v6i2.63020","DOIUrl":"https://doi.org/10.3126/jnms.v6i2.63020","url":null,"abstract":"In this paper, we study error estimates in the maximum norm in the context of solving Poisson’s equation numerically when approximated the Five-Point Laplacian method using the discrete maximum principle. The primary objective is to assess the accuracy of this numerical approach in solving Poisson’s equation and to provide insights into the behavior of error estimates. We focus on the estimates of maximum norm of the discrete functions defined on a grid in a unit square as well as in a square of side s, and estimate errors measured in the maximum norm.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"66 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140430375","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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