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Solving Nonlinear 1 st - order Ordinary Differential Equations (ODEs) using
Higher-Order Adams-Moulton Methods (AM)
Amira Natasha Binti Ismail
Supervisor: Dr. Loy Kak Choon
Bachelor of Science (Computational Mathematics)
School of Informatics and Applied Mathematics
In this project, we proposed the 1 st , 2 nd and 3 rd - order Adams-Moulton methods to solve
nonlinear 1 st - order ordinary differential equations (ODEs). These methods are chosen
since they are more stable than the explicit methods and can deal with stiff problems.
However, the disadvantage of using such implicit methods is that Newton’s method is
required to solve the resulting fixed point problems. We used two test cases comprised
of one test problem and one manufactured solution for the numerical illustration such as
to analyze the error and to reproduce the order of convergence as well as identifying the
L error
2
to ensure the solution exist. Finally, we captured the Central Processing Unit
(CPU) time to quantify the efficiency of AM methods of various order of convergence with
different step sizes by using Octave.
915 | UMT UNDERGRADUATE RESEARCH DAY 2018