Modified Asymmetric Schemes for Black -Scholes Equation of European Options Pricing System (Published)
In this paper, a fast numerical scheme for computing the European call options pricing problems governed by the Black Scholes equation was developed. Error analysis algorithm was developed from the proposed scheme. It is proved that the proposed scheme has second order accuracy in both time and space under some restrictions, the stability of the scheme in the sense of Non –Neumann analysis is presented. It is shown that the proposed scheme has a good performance in the sense of Errors, the computational cost and storage capacities compare to the Crank- Nicolson. Also the accuracy of the purposed scheme is better than the Semi- implicit scheme in most cases. Numerical examples are conducted to test the validity, efficiency, and accuracy of the proposed scheme.
Keywords: Asymmetric scheme, Black-Scholes equation, European option pricing, Numerical experiments., Stability analysis
MATHEMATICAL MODEL OF HIV/AIDS AT TECHIMAN MUNICIPALITY, GHANA (Published)
The study examined the prevalence of HIV/AIDS in the Techiman Municipality of Ghana. We used model with standard incidence to analyze, model and predict the prevalence of HIV/AIDS in the Techiman Municipality. The model has two equilibrium states: the disease-free equilibrium and the endemic equilibrium states respectively. The stability condition of each equilibrium point is discussed. The basic reproductive number ( ) of HIV/AIDS infection is estimated to be in the Techiman Municipality. Our work shows that the reproductive number of HIV/AIDS infection in the Techiman Municipality is less than 1( ) and therefore concluded that the disease is not epidemic in the municipality as described by the GAC in their study in 2005. We recommend that education on HIV/AIDS in the municipality should be intensified so as to decrease the rate of transmission of HIV in the municipality.
Keywords: Equilibrium points, Mathematical model, Model, Sensitivity Analysis, Stability analysis