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Semi-implicit Backward-Difference Formulae (SBDF) Methods for First-Order
Nonlinear Ordinary Differential Equations (ODEs)
Nurul Amira Eliana Binti Mohd Rahimi
Supervisor: Dr. Loy Kak Choon
Bachelor of Science (Computational Mathematics)
School of Informatics and Applied Mathematics
We proposed SBDF methods to solve nonlinear 1 st -order ordinary differential equations
(ODEs). SBDF methods which treat the linear term implicitly and the nonlinear term
explicitly are known to be more stable than fully explicit methods and at the same time
avoiding Newton’s method. However, they are less stable than the implicit methods. SBDF
methods are very efficient ODE solvers with a properly chosen step size. We found two
suitable well-posed test cases (test-problem and manufactured-solution) for the purpose
of numerical illustration. We derived SBDF methods using Taylor’s expansion and showed
the order of convergence theoretically. The exact solutions of the two test cases are
available for numerical benchmarking. We implement the numerical schemes using
Octave for two test cases using SBDF methods with 1 st -, 2 nd - and 3 rd -order of accuracy.
Also, the order of convergence was reproduced numerically and the CPU time for each
SBDF method is compared for efficiency analysis.
988 | UMT UNDERGRADUATE RESEARCH DAY 2018