dc.description.abstract | Youth unemployment is on the rise globally and it poses huge economic, social and political
challenges which results to unsustainable growth of the country’s economy. The
main aim of this thesis is to focus on youth unemployment in Kenya by developing a
mathematical model consisting of rst order systems of Ordinary Di erential Equations
(ODEs) and solve it numerically and to give results from mathematical perspective.Firstly,
we give introduction to Unemployment problem, ODEs, meaning of a solution to an ODE
and also conditions for a problem to satisfy for it to be referred as well posed. We then
discuss in brief analytical solution and also the numerical approach of nding a solution
to an ODE. A consideration of error analysis,convergence,consistency and stability of numerical
methods in general is discussed.
We consider Runge-Kutta (RK) methods of di erent orders, derivation of Euler methods,
second order,third order and RK method of fourth order are obtained and a brief formula
for fth order is given.Afterwards,error analysis for RK methods as well as the stability
analysis are discussed. After describing the methods for a single equation, we focus on
RK methods for solving systems of ODEs since it is our area of interest. We also analyze
the stability for one-step and multi-step methods for ODEs.
Once we are fully equipped with the necessary tools,we now obtained the numerical solution
the model using RK method of fourth order and discuss the results. | en_US |