This work delves into solving the two dimensional Poisson problem through the Finite Element Method which is relevant in various physical scenarios including heat conduction, electrostatics, gravity potential, and fluid dynamics. However, finding exact solutions to these problems can be complicated and challenging due to complexities in the domains such as re-entrant corners, cracks, and discontinuities of the solution along the boundaries, and due to the singular source function. Our focus in this work is to solve the Poisson equation in the presence of re entrant corners at the vertices of domain where some of the interior angles are greater than 180 degrees. When the domain features a re entrant corner, the numerical solution can display singular behavior near the corners. To address this, we propose a graded mesh algorithm that helps us to tackle the solution near singular points. We derive H1 and L2 error estimate results, and we use MATLAB to present numerical results that validate our theoretical findings. By exploring these concepts, we hope to provide new insights into the Poisson problem and inspire future research into the application of numerical methods to solve complex physical scenarios
{"title":"A Graded Mesh Refinement for 2D Poisson’s Equation on Non-Convex Polygonal Domains","authors":"Charuka D. Wickramasinghe, Priyanka Ahire","doi":"10.28924/APJM/11-63","DOIUrl":"https://doi.org/10.28924/APJM/11-63","url":null,"abstract":"This work delves into solving the two dimensional Poisson problem through the Finite Element Method which is relevant in various physical scenarios including heat conduction, electrostatics, gravity potential, and fluid dynamics. However, finding exact solutions to these problems can be complicated and challenging due to complexities in the domains such as re-entrant corners, cracks, and discontinuities of the solution along the boundaries, and due to the singular source function. Our focus in this work is to solve the Poisson equation in the presence of re entrant corners at the vertices of domain where some of the interior angles are greater than 180 degrees. When the domain features a re entrant corner, the numerical solution can display singular behavior near the corners. To address this, we propose a graded mesh algorithm that helps us to tackle the solution near singular points. We derive H1 and L2 error estimate results, and we use MATLAB to present numerical results that validate our theoretical findings. By exploring these concepts, we hope to provide new insights into the Poisson problem and inspire future research into the application of numerical methods to solve complex physical scenarios","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":" 26","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141681025","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}
{"title":"A Novel Numerical Algorithm for Singularly Perturbed Boundary Value Problems and Convergence Analysis Using Modified Haar Wavelet Method","authors":"","doi":"10.28924/apjm/10-22","DOIUrl":"https://doi.org/10.28924/apjm/10-22","url":null,"abstract":"","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69254198","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}
{"title":"Impact of Corruption in a Society With Exposed Honest Individuals: A Mathematical Model","authors":"Adetayo Samuel, Eegunjobi, O. Makinde","doi":"10.28924/apjm/10-18","DOIUrl":"https://doi.org/10.28924/apjm/10-18","url":null,"abstract":",","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69254587","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}
{"title":"On Fuzzy Closure Filters of Decomposable Stone Almost Distributive Lattices","authors":"","doi":"10.28924/apjm/10-40","DOIUrl":"https://doi.org/10.28924/apjm/10-40","url":null,"abstract":"","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135612360","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}
. Mathematical modeling is essential in both human and natural systems. In this work, we explore two prey and one predator models having Holling type I functional behaviors. We used a discrete-time delay to illustrate the permanence and boundedness of the system. We also characterized and displayed the stability and Hopf - Bifurcation for the competition model. Furthermore, we carried out the numerical simulation and experimental results to realize the impact of our model
{"title":"Analysis of Two Prey and One Predator Interaction Model With Discrete Time Delay","authors":"","doi":"10.28924/apjm/10-28","DOIUrl":"https://doi.org/10.28924/apjm/10-28","url":null,"abstract":". Mathematical modeling is essential in both human and natural systems. In this work, we explore two prey and one predator models having Holling type I functional behaviors. We used a discrete-time delay to illustrate the permanence and boundedness of the system. We also characterized and displayed the stability and Hopf - Bifurcation for the competition model. Furthermore, we carried out the numerical simulation and experimental results to realize the impact of our model","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136201868","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}
{"title":"Certain Regularity Results of p(x)-Parabolic Problems With Measure Data","authors":"","doi":"10.28924/apjm/10-1","DOIUrl":"https://doi.org/10.28924/apjm/10-1","url":null,"abstract":"","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69253954","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}
{"title":"A Weak Solution to a Non-Local Problem in Fractional Orlicz-Sobolev Spaces","authors":"","doi":"10.28924/apjm/10-2","DOIUrl":"https://doi.org/10.28924/apjm/10-2","url":null,"abstract":"","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69254612","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 an analysis of poverty dynamics in conjunction with populations affected by alcohol consumption using a deterministic perspective. A mathematical model is developed based on assumptions about the behaviour and challenges faced by individuals struggling with alcohol addiction and poverty. Our primary focus is examining how impoverished individuals can overcome alcohol addiction and reduce poverty within a specific area. We provide a comprehensive description of the model, emphasizing the existence and stability of different equilibria. Additionally, we conduct numerical simulations to assess the efficacy of our model. To further investigate the impact of critical parameters on the prevalence of illness and the basic reproduction number, we employ sensitivity analysis using PRCC. Our findings are illustrated through numerical simulations, effectively depicting the societal effects of alcohol and poverty through the mathematical model. We support our conclusions with suitable numerical explanations, utilizing visual representations of the respective compartments. We hope that our suggestions can contribute to effective poverty reduction strategies. 2020 Mathematics Subject Classification. 92B05, 34D20.
{"title":"Mathematical Modelling of the Drinking Behaviour Effect on Society","authors":"","doi":"10.28924/apjm/10-36","DOIUrl":"https://doi.org/10.28924/apjm/10-36","url":null,"abstract":". This paper presents an analysis of poverty dynamics in conjunction with populations affected by alcohol consumption using a deterministic perspective. A mathematical model is developed based on assumptions about the behaviour and challenges faced by individuals struggling with alcohol addiction and poverty. Our primary focus is examining how impoverished individuals can overcome alcohol addiction and reduce poverty within a specific area. We provide a comprehensive description of the model, emphasizing the existence and stability of different equilibria. Additionally, we conduct numerical simulations to assess the efficacy of our model. To further investigate the impact of critical parameters on the prevalence of illness and the basic reproduction number, we employ sensitivity analysis using PRCC. Our findings are illustrated through numerical simulations, effectively depicting the societal effects of alcohol and poverty through the mathematical model. We support our conclusions with suitable numerical explanations, utilizing visual representations of the respective compartments. We hope that our suggestions can contribute to effective poverty reduction strategies. 2020 Mathematics Subject Classification. 92B05, 34D20.","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135319130","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}
{"title":"Advanced Haar Wavelet Method With Its Convergence to the Bratu’s Type Numerical Boundary Value Problems","authors":"","doi":"10.28924/apjm/10-29","DOIUrl":"https://doi.org/10.28924/apjm/10-29","url":null,"abstract":"","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136201821","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：