Convex Regularization Method for Solving Cauchy Problem of the Helmholtz Equation

In this paper, we introduce the Convex Regularization Method (CRM) for regularizing the (instability) solution of the Helmholtz equation with Cauchy data. The CRM makes it possible for the solution of Helmholtz equation to depend continuously on the small perturbations in the Cauchy data. In addition, the numerical computation of the reg- ularized Helmholtz equation with Cauchy data is stable, accurate and gives high rate of convergence of solution in Hilbert space. Undoubtedly, the error estimated analysis associated with CRM is minimal.Mathematics Subject Classi cation: 44B28; 44B30Keywords: Convex Regularization Method, ill-posed Helmholtz equation with Cauchy data, stable solutio

A Two-Dimensional Chebyshev Wavelet Method for Solving Partial Di erential Equations

In this paper, we introduce a two-dimensional Chebyshev wavelet method (TCWM) for solving partial di erential equations (PDEs) in L2(R) space. In this method, the spatial variables appearing in the PDE each has its own kernel, as well as wavelet coecient for approxi- mating the unknown solution of the equation. The approximated solu- tion of the equation is fast and has higher number of vanishing moments as compared to the Chebyshev wavelet method with only one wavelet coecient for two or more separated kernels for the variables appearing in the PDE

A Fractional Differential Equation Modeling of SARS-CoV-2 (COVID-19) Disease in Ghana

The coronavirus (COVID-19) has spread through almost 224 countries and has caused over 5 million deaths. In this paper, we propose a model to study the transmission dynamics of COVID-19 in Ghana using fractional-derivatives. The fractional-derivative is defined in the Atangana Beleanu Caputo (ABC) sense. This model considers seven (7) classes namely; Susceptible individuals, Exposed, Asymptomatic population, Symptomatic, Vaccinated, Quarantined, and Recovered population. The equilibrium points, stability analysis, and the basic reproduction number of the model have been determined. The existence and uniqueness of the solution and Ulam Hyers stability are established. The model is tested using Ghana demographical and COVID-19 data. Further, two preventive control measures are incorporated into the model. The numerical analysis reveals the impact of the fractional-order derivative on the various classes of the disease model as one can get reliable information at any integer or non-integer value of the fractional operator. The results of the simulation predict the COVID-19 cases in Ghana. Analysis of the optimal control reveals social distancing leads to an increase in the susceptible population, whereas vaccination reduces the number of susceptible individuals. Both vaccination and social distancing lead to a decline in COVID-19 infections. It was established that the fractional-order derivatives could influence the behavior of all classes in the proposed COVID-19 disease model.Comment: The manuscript contains 21 figures and has 42 page

Macroscopic Analysis Of The Viscous-Diffusive Traffic Flow Model

Second-order macroscopic traffic models are characterized by a continuity equation and an acceleration equation. Convection, anticipation, relaxation, diffusion, and viscosity are the predominant features of the different classes of the acceleration equation. As a unique approach, this paper presents a new macro-model that accounts for all these dynamic speed quantities. This is done to determine the collective role of these traffic quantities in macroscopic modeling. The proposed model is solved numerically to explain some phenomena of a multilane traffic flow.  It also includes a linear stability analysis. Furthermore, the evolution of speed and density wave profiles are presented under the perturbation of some parameters

The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed Systems

This paper shows that discrete linear equations with Hilbert matrix operator, circulant matrix operator, conference matrix operator, banded matrix operator, TST matrix operator, and sparse matrix operator are ill-posed in the sense of Hadamard. Gauss least square method (GLSM), QR factorization method (QRFM), Cholesky decomposition method (CDM), and singular value decomposition (SVDM) failed to regularize these ill-posed problems. This paper introduces the eigenspace spectral regularization method (ESRM), which solves ill-posed discrete equations with Hilbert matrix operator, circulant matrix operator, conference matrix operator, and banded and sparse matrix operator. Unlike GLSM, QRFM, CDM, and SVDM, the ESRM regularizes such a system. In addition, the ESRM has a unique property, the norm of the eigenspace spectral matrix operator κK=K−1K=1. Thus, the condition number of ESRM is bounded by unity, unlike the other regularization methods such as SVDM, GLSM, CDM, and QRFM

A Genetic Algorithm for Option Pricing: The American Put Option

Abstract The search for a better option pricing model continues to find the one that outperforms the existing ones in the financial market. In this paper, we present a Genetic Algorithm (GA) to price a fixed term American put option when the underlying asset price is Geometric Brownian Motion. The Genetic Algorithm has a better approximation of the relationship between the option price and its contract terms. Our method produces a perfect and a minimum option price that outperforms other models like the Black-Scholes under the same conditions. The method requires 3198 J. Ackora-Prah, S. K. Amponsah, P. S. Andam and S. A Gyamera minimum assumptions and can easily adapt to changes and uncertainties in the financial environments

Kink collision in the noncanonical φ6 model: A model with localized inner structures

We study collisions of kinks in the one-space and one-time dimensional noncanonical nonintegrable scalar ϕ6 model. We examine the energy density of the kink, and we find that, as a function of the parameters that control the curvature of the potential, a localized inner structure of the energy density emerges. We also examine the kink excitation spectrum and the dynamics of the kink collisions for a wide range of initial velocities. We find that apart from the resonance windows, the production of two to three oscillons occurs for some values of the principal parameters of the model

A Proposed Method for Finding Initial Solutions to Transportation Problems

The Transportation Model (TM) in the application of Linear Programming (LP) is very useful in optimal distribution of goods. This paper focuses on finding Initial Basic Feasible Solutions (IBFS) to TMs hence, proposing a Demand-Based Allocation Method (DBAM) to solve the problem. This unprecedented proposal goes in contrast to the Cost-Based Resource Allocations (CBRA) associated with existing methods (including North-west Corner Rule, Least Cost Method and Vogel’s Approximation Method) which make cost cell (i.e. decision variable) selections before choosing demand and supply constraints. The proposed ‘DBAM’ on page 4 is implemented in MATLAB and has the ability to solve large-scale transportation problems to meet industrial needs. A sample of five (5) examples are presented to evaluate efficiency of the method. Initial Basic Feasible Solutions drawn from the study (according to DBAM) represent the optimal with higher accuracy, in comparison to the existing methods. Results from the study qualify the DBAM as one of the best methods to solve industrial transportation problems