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Runge-Kutta Methods for Solving
First-order Nonlinear Odes.
Ng Boon Wang
Supervisor: Dr. Loy Kak Choon
Bachelor of Science (Computational Mathematics)
School of Informatics and Applied Mathematics
Ordinary differential equations (ODEs) are encountered in various fields for solving
specific numerical problem. Numerical methods are used to understand and determine
the approximation solution close to exact solution of nonlinear ODEs. Runge-Kutta
methods (RK methods) are multistage methods which can efficiently produce high order
of accuracy or small magnitude of error. However, RK methods require relatively large
CPU time when achieve higher stage. We find two suitable test cases of numerical
illustration and calculate the CPU time to compare whether these methods are suitable
to solving nonlinear ODEs. When test problem from manufacturer solution, RK methods
achieve small error and higher order of convergence which is important to do error
analysis. When implementation of one exact solution and one manufacturer factor, we
proved the uniqueness for these two ODEs to ensure the solution exists. We implement
the code of two test cases comprise of test problem to analyse error.
958 | UMT UNDERGRADUATE RESEARCH DAY 2018