We prove the existence, the uniqueness and the boundedness of the solutions of the initial- boundary value problem for the ten velocity discrete model of gas C1 for bounded initial and boundary conditions.
This research was carried out to assess the ability of the students to apply calculus concepts to engineering problems. A sample of five (5) students was selected from each of the five departments in the college of engineering Waziri Umaru Federal Polytechnic, Birnin Kebbi giving a total of twenty five (25) students. Pearson correlation and paired samples t-test were used to analyze data using SPSS version 17.0. The results obtained indicated academic performance in calculus has a significant positive correlation with Calculus application to engineering problems (r = 0.693). A significant difference was observed in the mean score of Calculus Proficiency Test (mean 67.64, SD = 17.27) and Calculus Application Test (mean 53.48, SD = 13.58).
This paper considers the Differential Transform Method (DTM) for solving partial differential equations. The two-dimensional form of the method is used to solve a linear partial differential equation, a linearised version of the Korteweg-de Vries equation. The solutions are verified by solving the same equation using the Adomian Decomposition Method (ADM). The results also show that the DTM is much simpler to apply than the ADM.
Embedded in Life insurance contracts are surrender options and also path dependency. Surrender option stems from many reasons. Multi-morbidity increases the rate of mortality and a variety of adverse health outcomes which may lead to surrendering. Poverty levels coupled with social burdens can inform a multi-morbid person to surrender a life policy contract. The study seeks determine and compare valuation of options of a multi-morbid person surrendering. In line with this objective the multi-morbid survival rate of a policy holder was incorporated in the Black- Scholes model for option pricing. The solution to the model come with its own complexities, therefore the need to resort to numerical solutions for the option valuation. Further, a comparison is made of two finite difference algorithm in solving the proposed Black-Scholes equation; the Crank-Nicolson method and the Hopscotch method. Simulations of survival were performed tocompute the survival rate. Numerical solution to the Black-Scholes model and the proposed model indicates that the Crank-Nicolson method converges faster than the Hopscotch method for the Black-Scholes whiles the Hopscotch method converges faster than the Crank-Nicolson for the proposed modified Black-Scholes model. It was observed that the Hopscotch method converges faster as the multi-morbid survival rate decreases below the short rate of the Black-Scholes model.
In this paper, an implicit k-step linear multi-step methods using the Laguerre polynomials as the basis functions is proposed. The given discrete methods were used in block and implemented for solving the initial value problems, being continuous interpolant derived and collocated at grid points. Numerical examples of initial value problems (IVPs) of ordinary differential equations (ODEs) were solved using the derived methods, and it is observed that the results obtained converged faster and the consistency and the zero stability are validated.