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The Combination of Exponential Integrator and Multistep Methods for
1 st -order Nonlinear Ordinary Differential Equations (ODEs)
Fatin Farehah Binti Zamri
Supervisor: Dr. Loy Kak Choon
Bachelor of Science (Computational Mathematics)
School of Informatics and Applied Mathematics
We proposed an Exponential Integrator method (EIM) combining with Adams Bashforth
approach to solve the nonlinear 1 st – order ODEs. We investigated the property of the
numerical error, convergence and efficiency of the resulted methods. For instance, they
were thoroughly assessed using test problems. EIM is more stable than many explicit
methods since the methods solve the linear part using exact integration and the
interpolation strategy only for the nonlinear part. High – order Adams Bashforth methods
are also combined with EIM to produce higher-order schemes for better accuracy to the
numerical solution. These numerical schemes are implement using Octave programming
language. The major contribution of this research project is to introduce more stable
methods while still being explicit to solve various models associating with first-order
nonlinear ODEs.
925 | UMT UNDERGRADUATE RESEARCH DAY 2018