A Two-parameter Family of Exponentially-fitted Obrechkoff Methods for Second-order Boundary Value Problems
Ashiribo Senapon Wusu1
1Department Of Mathematics, Lagos State University, Nigeria
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.
Multiparameter, Exponentially--fitted, Obrechkoff Method, Oscillatory, and Periodic