Abstract

Introduction: Generally, classical numerical methods may not be well suited for problems with oscillatory or periodic behaviour. To overcome this deficiency, they are modified using a technique called exponential fittings. The modification makes it possible to construct new methods suitable for the efficient integration of oscillatory or periodic problems from classical ones. Aims: In this work, a two–parameter family of exponentially–fitted Obrechkoff methods for approaching problems that exhibit oscillatory or periodic behaviour is constructed. Materials and Methods: The construction is based on a six­step flowchart described in the literature. Results: Unlike the single–frequency method in the literature, the constructed methods depend upon two frequencies which can be tuned to solve the problem at hand more accurately. The leading term of the local truncation error of the new family of method can also be easily obtained from the given general expression. The efficiency of the new methods is demonstrated on some numerical examples Conclusion: This work provides extension to the results obtained in by authors in the literature.

Keywords: Multiparameter, Exponentially--fitted, Obrechkoff Method, Oscillatory, and Periodic