merged

Solving Nonlinear 1 st -Order Ordinary Differential Equations (ODEs) using
Adams-Bashforth Methods
Nurul Atikah Binti Ruslan
Supervisor: Dr. Loy Kak Choon
Bachelor of Science (Computational Mathematics)
School of Informatics and Applied Mathematics
Numerical method are viable mathematical tools to solve the ordinary differential
equations (ODE) that appears in various modelling problems. We proposed fully explicit
Adams-Bashforth (AB) methods are to solve the nonlinear 1 st -order ODEs. AB methods
are very efficient and easy to implement since they do not require Newton’s method. AB
methods on the other hand are conditionally stable and less robust to handle stiff
problem. We derived the AB methods and showed the order of convergence theoretically.
We used two test cases comprises of one test problem and one manufactured solution
for the purpose of numerical illustration. We solved two test cases using AB methods with
1 st -, 2 nd -, and 3 rd -order of accuracy via Octave. Lastly, we analyzed the error, reproduced
the order of convergence and captured the CPU time for efficiency analysis.
989 | UMT UNDERGRADUATE RESEARCH DAY 2018