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Abstract:
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This thesis looks at the numerical solution of the Riccati Equation y0 = 1 - y2, which has a known analytical solution. This equation is converted into a two-point boundary value problem before being analyzed as an initial value problem. First- order Ordinary Differential Equations (ODE) solvers, that minimize inherent error, are tailored to the Ricatti equation. We focus on finding the value of theta that would minimize the inherent error of the Theta Method. Random switching is then done between implicit and explicit numerical methods and error analysis is conducted on this switching method. Here we are interested in whether or not random switching produces more accurate results (smallest inherent error) than the individual methods. |