The Sharma–Tasso–Olver–Burgers equation: Its conservation laws and kink solitons

The present paper deals with the Sharma–Tasso–Olver–Burgers equation (STOBE) and its conservation laws and kink solitons. More precisely, the formal Lagrangian, Lie symmetries, and adjoint equations of the STOBE are firstly constructed to retrieve its conservation laws. Kink solitons of the STOBE are then extracted through adopting a series of newly well-designed approaches such as Kudryashov and exponential methods. Diverse graphs in 3D postures are formally portrayed to reveal the dynamical features of kink solitons. According to the authors’ knowledge, the outcomes of the current investigation are new and have been listed for the first time.

Optical Solitons to the Ginzburg–Landau Equation Including the Parabolic Nonlinearity

The major goal of the present paper is to construct optical solitons of the Ginzburg–Landau (GL) equation including the parabolic nonlinearity. Such an ultimate goal is formally achieved with the aid of symbolic computation, a complex transformation, and Kudryashov and exponential methods. Several numerical simulations are given to explore the influence of the coefficients of nonlinear terms on the dynamical features of the obtained optical solitons. To the best of the authors’ knowledge, the results reported in the current study, classified as bright and kink solitons, are new and have been acquired for the first time.

Breaking theory of solitary waves for the Riemann wave equation in fluid dynamics

In this study, analytical solutions and physical interpretations are presented for the Riemann wave equation (RWE), which has an important physical property in fluid dynamics. The solutions of the RWE, which models the formation, interaction and breaking of the waves that occur as a result of any external effect on the ocean surface, are examined using the generalized exponential rational function method (GERFM). Bright (nontopological) soliton, singular soliton and solitary wave solutions are produced with advantages of GERFM over other traditional exponential methods. The factors in which solitary wave solutions cause breaking of wave are examined. The effects of parameters on wavefunctions and the physical interpretations of these effects are discussed and supported by graphics and simulations.

Why Improving the Accuracy of Exponential Integrators Can Decrease Their Computational Cost?

In previous papers, a technique has been suggested to avoid order reduction when integrating initial boundary value problems with several kinds of exponential methods. The technique implies in principle to calculate additional terms at each step from those already necessary without avoiding order reduction. The aim of the present paper is to explain the surprising result that, many times, in spite of having to calculate more terms at each step, the computational cost of doing it through Krylov methods decreases instead of increases. This is very interesting since, in that way, the methods improve not only in terms of accuracy, but also in terms of computational cost.

MATRIX EXPONENTIAL METHODS FOR PARALLEL COMPUTING OF ISOTOPIC DEPLETION AND SPECIES TRANSPORT FOR MOLTEN SALT REACTOR ANALYSIS

Matrix exponential methods have long been utilized for isotopic depletion in nuclear fuel calculations. In this paper we discuss the development of such methods in addition to species transport for liquid fueled molten salt reactors (MSRs). Conventional nuclear reactors work with fixed fuel assemblies in which fission products and fissile material do not transport throughout the core. Liquid fueled molten salt reactors work in a much different way, allowing for material to transport throughout the primary reactor loop. Because of this, fission product transport must be taken into account. The set of partial differential equations that apply are discretized into systems of first order ordinary differential equations (ODEs). The exact solution to the set of ODEs is herein being estimated using the matrix exponential method known as the Chebychev Rational Approximation Method (CRAM).

The spread of COVID-19 outbreak in the first 120 days: A comparison between Nigeria and seven other countries

Background: COVID-19 is an emerging global public health crisis. The increase in the daily COVID-19 confirmed cases in Nigeria is worrisome vis-a-vis its large and dense population. This study aims at assessing the pattern of spread in the first 120 days of COVID-19 case confirmation in Nigeria, and its comparison with seven other countries. Methods: Data extracted from the World Bank’s website were used for the descriptive assessment and modelling of COVID-19 disease using the first 120 days of the index case in Nigeria and seven other countries. Linear, quadratic, cubic and exponential methods of regression model were used to fit the data (α=0.05). Results: The COVID-19 growth pattern in Nigeria was similar to that of Egypt, Ghana and Cameroun; Nigeria’s COVID-19 daily death distribution was comparable to six of the other seven countries considered. There was an increasing trend in the daily COVID-19 confirmed cases in Nigeria. During the lockdown, the growth rate of COVID-19 in Nigeria was 5.85 (R2=0.728, p<0.001); however, it was 8.42 (R2=0.625, p<0.001) after the lockdown relaxation. Across all the countries investigated, the cubic polynomial model (CPM) provided the best fit for predicting COVID-19 cumulative cases and there was a clear deviation from the exponential growth model. Using the CPM, all things being equal, a 3-month (30 September 2020) prediction of COVID-19 cases in Nigeria was 155,467 (95% CI:151,111-159,824, p<0.001). Conclusions: An improvement in COVID-19 control measures and strict compliance with the COVID-19 recommended protocols are essential. A contingency plan is needed to provide care for the active cases in case the predicted target is realised.

The spread of COVID-19 outbreak in the first 120 days: A comparison between Nigeria and seven other countries

Background: COVID-19 is an emerging global public health crisis. The increase in the daily COVID-19 confirmed cases in Nigeria is worrisome vis-a-vis its large and dense population. This study aims at assessing the pattern of spread in the first 120 days of COVID-19 case confirmation in Nigeria, and its comparison with seven other countries. Methods: Data extracted from the World Bank’s website were used for the descriptive assessment and modelling of COVID-19 disease using the first 120 days of the index case in Nigeria and seven other countries. Linear, quadratic, cubic and exponential methods of regression model were used to fit the data (α=0.05). Results: The COVID-19 growth pattern in Nigeria was similar to that of Egypt, Ghana and Cameroun; Nigeria COVID-19's daily death distribution was comparable to six of the other seven countries considered. There was an increasing trend in the daily COVID-19 confirmed cases in Nigeria. During the lockdown, the growth rate of COVID-19 in Nigeria was 5.85 (R2=0.728, p<0.001); however, it was 8.42 (R2=0.625, p<0.001) after the lockdown’s relaxation. Across all the countries investigated, the cubic polynomial model (CPM) provided the best fit for predicting COVID-19 cumulative cases and there was a clear deviation from the exponential growth model. Using the CPM, all things being equal, a 3-month (30 September 2020) prediction of COVID-19 cases in Nigeria was 155,467 (95% CI:151,111-159,824, p<0.001). Conclusions: An improvement in COVID-19 control measures and strict compliance with the COVID-19 recommended protocols are essential. A contingency plan is needed to provide care for the active cases in case the predicted target is realised.

Comparing with other countries the spread of COVID-19 within the first 120 days of its outbreak in Nigeria

Background: COVID-19 is an emerging global public health crisis. The increase in the daily COVID-19 confirmed cases in Nigeria is worrisome vis-a-vis its large and dense population. This study aims at assessing the first 120 days of COVID-19 case confirmation in Nigeria.Methods: Data extracted from the World Bank’s website were used for the descriptive assessment and modelling of COVID-19 disease using the first 120 days of the index case in Nigeria and seven other countries. Linear, quadratic, cubic and exponential methods of regression model were used to fit the data (α=0.05).Results: The COVID-19 growth pattern in Nigeria was similar to that of Egypt, Ghana and Cameroun; Nigeria COVID-19's daily death distribution was comparable to six of the other seven countries considered. There was an increasing trend in the daily COVID-19 confirmed cases in Nigeria. During the lockdown, the growth rate of COVID-19 in Nigeria was 5.85 (R2=0.728, p<0.001); however, it was 8.42 (R2=0.625, p<0.001) after the lockdown’s relaxation. Across all the countries investigated, the cubic polynomial model (CPM) provided the best fit for predicting COVID-19 cumulative cases and there was a clear deviation from the exponential growth model. Using the CPM, all things being equal, a 3-month (30 September 2020) prediction of COVID-19 cases in Nigeria was 155,467 (95% CI:151,111-159,824, p<0.001).Conclusions: An improvement in COVID-19 control measures and strict compliance with the COVID-19 recommended protocols are essential. A contingency plan is needed to provide care for the active cases in case the predicted target is realised.