Technical report: numerical solutions of Riccati equations using Adam-Bashforth and Adam-Moulton methods / Mohamad Nazri Mohamad Khata, Nur Habibah Radzali and Mohamad Aliff Afifuddin Hilmy - Khata, Mohamad Nazri Mohamad; Radzali, Nur Habibah; Hilmy, Mohamad Aliff Afifuddin (2017)
A differential equation can be solved analytically or numerically. In many complicated cases, it is enough to just approximate the solution if the differential equation cannot be solved analytically. Euler's method, the improved Euler's method and Runge-Kutta methods are examples of commonly used numerical techniques in approximately solved differential equations. These methods are also called as single-step methods or starting methods because they use the value from one starting step to approximate the solution of the next step. While, multistep or continuing methods such as Adam-Bashforth and Adam-Moulton methods use the values from several computed steps to approximate the value of the next step. So, in terms of minimizing the calculating time in solving differential , multistep method is recommended by previous researchers. In this project, a Riccati differential equation is solved using the two multistep methods in order to analyze the accuracy of both methods. Both methods give small errors when they are compared to the exact solution but it is identified that Adam-Bashforth method is more accurate than Adam-Moulton method.