Mathematical Modelling and Numerical Simulation with Applications最新文献

Spectral collocation with generalized Laguerre operational matrix for numerical solutions of fractional electrical circuit models 使用广义拉盖尔运算矩阵的谱配位，用于分数电路模型的数值求解

Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2024-03-31 DOI: 10.53391/mmnsa.1428035

İbrahim Avcı

{"title":"Spectral collocation with generalized Laguerre operational matrix for numerical solutions of fractional electrical circuit models","authors":"İbrahim Avcı","doi":"10.53391/mmnsa.1428035","DOIUrl":"https://doi.org/10.53391/mmnsa.1428035","url":null,"abstract":"In this paper, we introduce a pioneering numerical technique that combines generalized Laguerre polynomials with an operational matrix of fractional integration to address fractional models in electrical circuits. Specifically focusing on Resistor-Inductor ($RL$), Resistor-Capacitor ($RC$), Resonant (Inductor-Capacitor) ($LC$), and Resistor-Inductor-Capacitor ($RLC$) circuits within the framework of the Caputo derivative, our approach aims to enhance the accuracy of numerical solutions. We meticulously construct an operational matrix of fractional integration tailored to the generalized Laguerre basis vector, facilitating a transformation of the original fractional differential equations into a system of linear algebraic equations. By solving this system, we obtain a highly accurate approximate solution for the electrical circuit model under consideration. To validate the precision of our proposed method, we conduct a thorough comparative analysis, benchmarking our results against alternative numerical techniques reported in the literature and exact solutions where available. The numerical examples presented in our study substantiate the superior accuracy and reliability of our generalized Laguerre-enhanced operational matrix collocation method in effectively solving fractional electrical circuit models.","PeriodicalId":484817,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"114 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140360338","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}

引用次数: 0

A fractional mathematical model approach on glioblastoma growth: tumor visibility timing and patient survival 胶质母细胞瘤生长的分数数学模型方法：肿瘤可见时间与患者生存率

Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2024-03-29 DOI: 10.53391/mmnsa.1438916

Nurdan Kar, N. Ozalp

{"title":"A fractional mathematical model approach on glioblastoma growth: tumor visibility timing and patient survival","authors":"Nurdan Kar, N. Ozalp","doi":"10.53391/mmnsa.1438916","DOIUrl":"https://doi.org/10.53391/mmnsa.1438916","url":null,"abstract":"In this paper, we introduce a mathematical model given by \u0000begin{equation} \u0000 { }^c mathfrak{D}_t^alpha u = nabla cdot mathrm{D} nabla u + rho f(u) quad text{in } Omega, \u0000end{equation} \u0000where $f(u)=frac{1}{1-u/mathrm{K}}, , u/mathrm{K} neq 1, , mathrm{K} > 0$, to enhance established mathematical methodologies for better understanding glioblastoma dynamics at the macroscopic scale. The tumor growth model exhibits an innovative structure even within the conventional framework, including a proliferation term, $f(u)$, presented in a different form compared to existing macroscopic glioblastoma models. Moreover, it represents a further refined model by incorporating a calibration criterion based on the integration of a fractional derivative, $alpha$, which differs from the existing models for glioblastoma. Throughout this study, we initially discuss the modeling dynamics of the tumor growth model. Given the frequent recurrence observed in glioblastoma cases, we then track tumor mass formation and provide predictions for tumor visibility timing on medical imaging to elucidate the recurrence periods. Furthermore, we investigate the correlation between tumor growth speed and survival duration to uncover the relationship between these two variables through an experimental approach. To conduct these patient-specific analyses, we employ glioblastoma patient data and present the results via numerical simulations. In conclusion, the findings on tumor visibility timing align with empirical observations, and the investigations into patient survival further corroborate the well-established inter-patient variability for glioblastoma cases.","PeriodicalId":484817,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"45 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140365302","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}

引用次数: 0

Free convection at different locations of adiabatic elliptic blockage in a square enclosure 方形围墙内绝热椭圆形堵塞物不同位置的自由对流

Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2024-03-28 DOI: 10.53391/mmnsa.1382516

M. Fayz-al-asad

引用次数: 0

A novel Touchard polynomial-based spectral matrix collocation method for solving the Lotka-Volterra competition system with diffusion 一种新颖的基于Touchard多项式的谱矩阵配位法，用于求解带扩散的Lotka-Volterra竞争系统

Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2024-03-09 DOI: 10.53391/mmnsa.1408997

M. Izadi, A. El-mesady, W. Adel

引用次数: 0

Mathematical approaches to controlling COVID-19: optimal control and financial benefits 控制 COVID-19 的数学方法：最佳控制和经济效益

Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2024-01-21 DOI: 10.53391/mmnsa.1373093

Saida Id Ouaziz, Mohammed El Khomssi

{"title":"Mathematical approaches to controlling COVID-19: optimal control and financial benefits","authors":"Saida Id Ouaziz, Mohammed El Khomssi","doi":"10.53391/mmnsa.1373093","DOIUrl":"https://doi.org/10.53391/mmnsa.1373093","url":null,"abstract":"The global population has suffered extensively as an effect of the coronavirus infection, with the loss of many lives, adverse financial consequences, and increased impoverishment. In this paper, we propose an example of the non-linear mathematical modeling of the COVID-19 phenomenon. Using the fixed point theorem, we established the solution's existence and unicity. We demonstrate how, under the framework, the basic reproduction number can be redefined. The different equilibria of the model are identified, and their stability analyses are carefully examined. According to our argument, it is illustrated that there is a single optimal control that can be used to reduce the expense of the illness load and applied processes. The determination of optimal strategies is examined with the aid of Pontryagin's maximum principle. To support the analytical results, we perform comprehensive digital simulations using the Runge-Kutta 4th-order. The data simulated suggest that the effects of the recommended controls significantly impact the incidence of the disease, in contrast to the absence of control cases. Further, we calculate the incremental cost-effectiveness ratio to assess the cost and benefits of each potential combination of the two control measures. The findings indicate that public attention, personal hygiene practices, and isolating oneself will all contribute to slowing the spread of COVID-19. Furthermore, those who are infected can readily decrease their virus to become virtually non-detectable with treatment consent.","PeriodicalId":484817,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140501259","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}

引用次数: 0

A harmonic oscillator model of atmospheric dynamics using the Newton-Kepler planetary approach 使用牛顿-开普勒行星方法的大气动力学谐振子模型

Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2023-09-30 DOI: 10.53391/mmnsa.1332893

Alexander MUNSON

{"title":"A harmonic oscillator model of atmospheric dynamics using the Newton-Kepler planetary approach","authors":"Alexander MUNSON","doi":"10.53391/mmnsa.1332893","DOIUrl":"https://doi.org/10.53391/mmnsa.1332893","url":null,"abstract":"Projection of future meteorological patterns such as median temperature and precipitation are necessary for governments to facilitate civil aviation, forecast agricultural productions, and advise future public energy policies. Various models were proposed based on historical data such as the short-term 7-day forecast or the long-term Global Forecast System to study climate change over the coming decades. We strike a balance by examining the harmonic oscillator model in mid-term weather projections. This model is the starting point to provide general mathematical guidelines to inform governmental agencies to forecast levels of energy consumptions for residential cooling in summer and heating in winter to provide energy subsidies for low-income populations and for non-profit organizations to support countries needing energy assistance. Additionally, mid-term meteorological models are especially useful during time of global energy disruptions. A model is derived based on orbital mechanics, planetary science, and astronomy using Newton’s Law of Universal Gravitation and Kepler’s Laws of Planetary Motions. We optimize the model with historical data on a specific region. The model’s predictions were then statistically compared with the actual data in the same time period in the region in a reverse goodness of fit test. We also gave certain directions on the generalized harmonic oscillator model in the future. In sum, the current harmonic oscillator method can be beneficially utilized by governments to forecast natural phenomena in order to provide timely assistance to respective populations such as in the control of infectious diseases or predicting extreme temperature fluctuations in the planning of agricultural productions.","PeriodicalId":484817,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136280181","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}

引用次数: 0

Two-dimensional Cattaneo-Hristov heat diffusion in the half-plane 半平面上二维Cattaneo-Hristov热扩散

Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2023-09-30 DOI: 10.53391/mmnsa.1340302

Beyza Billur İSKENDER EROĞLU

引用次数: 0

Understanding the mathematical background of Generative Adversarial Networks (GANs) 理解生成对抗网络(GANs)的数学背景

Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2023-09-30 DOI: 10.53391/mmnsa.1327485

Bilgi YILMAZ, Ralf KORN

引用次数: 1

Optical solitons of the complex Ginzburg-Landau equation having dual power nonlinear form using $varphi ^{6}$-model expansion approach 利用$varphi ^{6}$-模型展开方法求解具有对偶幂次非线性形式的复Ginzburg-Landau方程的光学孤子

Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2023-09-30 DOI: 10.53391/mmnsa.1337648

Muhammad Abubakar ISAH, Asıf YOKUŞ

引用次数: 0

Mathematical dynamics for HIV infections with public awareness and viral load detectability 艾滋病毒感染的数学动力学与公众意识和病毒载量检测

Mathematical Modelling and Numerical Simulation with Applications Pub Date : 2023-09-30 DOI: 10.53391/mmnsa.1349472

Umar Tasiu MUSTAPHA, Abdurrahman ADO, Abdullahi YUSUF, Sania QURESHİ, Salihu Sabiu MUSA

引用次数: 0