Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nat...Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nations.Following WHO(World health organization)records on 30 December 2021,the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266,active,recovered,and discharge were found to be 82,402 and 34,258,778,respectively.While there were 160,989 active cases,33,614,434 cured cases,456,386 total deaths,and 605,885,769 total samples tested.So far,1,438,322,742 individuals have been vaccinated.The coronavirus or COVID-19 is inciting panic for several reasons.It is a new virus that has affected the whole world.Scientists have introduced certain ways to prevent the virus.One can lower the danger of infection by reducing the contact rate with other persons.Avoiding crowded places and social events withmany people reduces the chance of one being exposed to the virus.The deadly COVID-19 spreads speedily.It is thought that the upcoming waves of this pandemicwill be evenmore dreadful.Mathematicians have presented severalmathematical models to study the pandemic and predict future dangers.The need of the hour is to restrict the mobility to control the infection from spreading.Moreover,separating affected individuals from healthy people is essential to control the infection.We consider the COVID-19 model in which the population is divided into five compartments.The present model presents the population’s diffusion effects on all susceptible,exposed,infected,isolated,and recovered compartments.The reproductive number,which has a key role in the infectious models,is discussed.The equilibrium points and their stability is presented.For numerical simulations,finite difference(FD)schemes like nonstandard finite difference(NSFD),forward in time central in space(FTCS),and Crank Nicolson(CN)schemes are implemented.Some core characteristics of schemes like stability and consistency are calculated.展开更多
This research paper represents a numerical approximation to three interesting equations of Fisher, which are linear, non-linear and coupled linear one dimensional reaction diffusion equations from population genetics....This research paper represents a numerical approximation to three interesting equations of Fisher, which are linear, non-linear and coupled linear one dimensional reaction diffusion equations from population genetics. We studied accuracy in term of L∞ error norm by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension non-linear reaction diffusion equations.展开更多
In this paper, we originate results with finite difference schemes to approximate the solution of the classical Fisher Kolmogorov Petrovsky Piscounov (KPP) equation from population dynamics. Fisher’s equation describ...In this paper, we originate results with finite difference schemes to approximate the solution of the classical Fisher Kolmogorov Petrovsky Piscounov (KPP) equation from population dynamics. Fisher’s equation describes a balance between linear diffusion and nonlinear reaction. Numerical example illustrates the efficiency of the proposed schemes, also the Neumann stability analysis reveals that our schemes are indeed stable under certain choices of the model and numerical parameters. Numerical comparisons with analytical solution are also discussed. Numerical results show that Crank Nicolson and Richardson extrapolation are very efficient and reliably numerical schemes for solving one dimension fisher’s KPP equation.展开更多
When filling embankment dams in cold regions,engineers must solve two freeze–thaw cycle(FTC)-induced soil problems.First,compacted soil constituting the dam is subjected to the FTC during dam construction.Second,loos...When filling embankment dams in cold regions,engineers must solve two freeze–thaw cycle(FTC)-induced soil problems.First,compacted soil constituting the dam is subjected to the FTC during dam construction.Second,loose soil material(LSM),which is subjected to the FTC,fills the dam.To investigate the effects of the aforementioned two problems on the hydraulic conductivity of compacted clayey soil,a series of permeation tests on clayey soil compacted before and after FTC were conducted in this study.The results showed that for the first problem,the hydraulic conductivity of compacted clayey soil subjected to one FTC significantly increases by two to three orders of magnitude because FTC-induced cracks can cause preferential flow in the permeation process.For the second problem,when the FTC number is less than a critical number,the FTC of the LSM may result in the development of united soil particles,thereby increasing the effective porosity ratio and hydraulic conductivity of the compacted soil.It was discovered that the hydraulic conductivity of compacted soil can increase by one to three times when the LSM is subjected to 10 FTCs.When the FTC number exceeds a critical number,the effective porosity ratio and hydraulic conductivity of the compacted soil may decrease with the FTC of the LSM.This should be investigated in future studies,and the results can be used to improve engineering management processes when filling embankment dams during winter in cold regions.展开更多
This research paper represents a numerical approximation to non-linear two-dimensional reaction diffusion equation from population genetics. Since various initial and boundary value problems exist in two-dimensional r...This research paper represents a numerical approximation to non-linear two-dimensional reaction diffusion equation from population genetics. Since various initial and boundary value problems exist in two-dimensional reaction-diffusion, phenomena are studied numerically by different numerical methods, here we use finite difference schemes to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension nonlinear reaction diffusion equations with a little modification.展开更多
This research paper represents a numerical approximation to non-linear coupled one dimension reaction diffusion system, which includes the existence and uniqueness of the time dependent solution with upper and lower b...This research paper represents a numerical approximation to non-linear coupled one dimension reaction diffusion system, which includes the existence and uniqueness of the time dependent solution with upper and lower bounds of the solution. Also numerical approximation is obtained by finite difference schemes to reach at reasonable level of accuracy, which is magnified by L2, L∞ and relative error norms. The accuracy of the approximations is shown by randomly selected grid points along time level and comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Moreover, the schemes can be easily applied to a wide class of higher dimension non-linear reaction diffusion equations with a little modifications.展开更多
基金supported by the research grants Seed ProjectPrince Sultan UniversitySaudi Arabia SEED-2022-CHS-100.
文摘Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nations.Following WHO(World health organization)records on 30 December 2021,the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266,active,recovered,and discharge were found to be 82,402 and 34,258,778,respectively.While there were 160,989 active cases,33,614,434 cured cases,456,386 total deaths,and 605,885,769 total samples tested.So far,1,438,322,742 individuals have been vaccinated.The coronavirus or COVID-19 is inciting panic for several reasons.It is a new virus that has affected the whole world.Scientists have introduced certain ways to prevent the virus.One can lower the danger of infection by reducing the contact rate with other persons.Avoiding crowded places and social events withmany people reduces the chance of one being exposed to the virus.The deadly COVID-19 spreads speedily.It is thought that the upcoming waves of this pandemicwill be evenmore dreadful.Mathematicians have presented severalmathematical models to study the pandemic and predict future dangers.The need of the hour is to restrict the mobility to control the infection from spreading.Moreover,separating affected individuals from healthy people is essential to control the infection.We consider the COVID-19 model in which the population is divided into five compartments.The present model presents the population’s diffusion effects on all susceptible,exposed,infected,isolated,and recovered compartments.The reproductive number,which has a key role in the infectious models,is discussed.The equilibrium points and their stability is presented.For numerical simulations,finite difference(FD)schemes like nonstandard finite difference(NSFD),forward in time central in space(FTCS),and Crank Nicolson(CN)schemes are implemented.Some core characteristics of schemes like stability and consistency are calculated.
文摘This research paper represents a numerical approximation to three interesting equations of Fisher, which are linear, non-linear and coupled linear one dimensional reaction diffusion equations from population genetics. We studied accuracy in term of L∞ error norm by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension non-linear reaction diffusion equations.
文摘In this paper, we originate results with finite difference schemes to approximate the solution of the classical Fisher Kolmogorov Petrovsky Piscounov (KPP) equation from population dynamics. Fisher’s equation describes a balance between linear diffusion and nonlinear reaction. Numerical example illustrates the efficiency of the proposed schemes, also the Neumann stability analysis reveals that our schemes are indeed stable under certain choices of the model and numerical parameters. Numerical comparisons with analytical solution are also discussed. Numerical results show that Crank Nicolson and Richardson extrapolation are very efficient and reliably numerical schemes for solving one dimension fisher’s KPP equation.
基金supported by the National Natural Science Foundation of China(Grant No.41801039,42071095,41771066)the Second Tibetan Plateau ReferencesScientific Expedition and Research(STEP)program(Grant No.2019QZKK0905)+1 种基金the Science and Technology Project of Gansu Province(Grant No.21JR7RA052)the Science and Technology Project of Yalong River Hydropower Development Company(LHKA-G201906)。
文摘When filling embankment dams in cold regions,engineers must solve two freeze–thaw cycle(FTC)-induced soil problems.First,compacted soil constituting the dam is subjected to the FTC during dam construction.Second,loose soil material(LSM),which is subjected to the FTC,fills the dam.To investigate the effects of the aforementioned two problems on the hydraulic conductivity of compacted clayey soil,a series of permeation tests on clayey soil compacted before and after FTC were conducted in this study.The results showed that for the first problem,the hydraulic conductivity of compacted clayey soil subjected to one FTC significantly increases by two to three orders of magnitude because FTC-induced cracks can cause preferential flow in the permeation process.For the second problem,when the FTC number is less than a critical number,the FTC of the LSM may result in the development of united soil particles,thereby increasing the effective porosity ratio and hydraulic conductivity of the compacted soil.It was discovered that the hydraulic conductivity of compacted soil can increase by one to three times when the LSM is subjected to 10 FTCs.When the FTC number exceeds a critical number,the effective porosity ratio and hydraulic conductivity of the compacted soil may decrease with the FTC of the LSM.This should be investigated in future studies,and the results can be used to improve engineering management processes when filling embankment dams during winter in cold regions.
文摘This research paper represents a numerical approximation to non-linear two-dimensional reaction diffusion equation from population genetics. Since various initial and boundary value problems exist in two-dimensional reaction-diffusion, phenomena are studied numerically by different numerical methods, here we use finite difference schemes to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension nonlinear reaction diffusion equations with a little modification.
文摘This research paper represents a numerical approximation to non-linear coupled one dimension reaction diffusion system, which includes the existence and uniqueness of the time dependent solution with upper and lower bounds of the solution. Also numerical approximation is obtained by finite difference schemes to reach at reasonable level of accuracy, which is magnified by L2, L∞ and relative error norms. The accuracy of the approximations is shown by randomly selected grid points along time level and comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Moreover, the schemes can be easily applied to a wide class of higher dimension non-linear reaction diffusion equations with a little modifications.
