Abstract
Abstract The exponential spline function is presented to find the numerical solution of third-order singularly perturbed boundary value problems. Convergence analysis of the method is briefly discussed, and it is shown to be sixth order convergence. To validate the applicability of the method, some model problems are solved for different values of the perturbation parameter, and the numerical results are presented both in tables and graphs. Furthermore, the present method gives more accurate solution than some methods existing in the literature.
Highlights
Perturbed problems arise frequently in the mathematical modelling of real-life phenomena in science and engineering areas such as fluid mechanics, elasticity, quantum mechanics, chemical-reactor theory, aerodynamics, plasma dynamics, rarefied-gas dynamics, oceanography, meteorology, modelling of semiconductor devices, geophysics, optimal control theory, diffraction theory and reaction–diffusion processes [1,2]
The exponential spline method is developed to approximate solution of a third-order singularly perturbed two point boundary value problems
The convergence analysis is investigated and revealed that the present method is of sixth order convergence
Summary
Perturbed problems arise frequently in the mathematical modelling of real-life phenomena in science and engineering areas such as fluid mechanics, elasticity, quantum mechanics, chemical-reactor theory, aerodynamics, plasma dynamics, rarefied-gas dynamics, oceanography, meteorology, modelling of semiconductor devices, geophysics, optimal control theory, diffraction theory and reaction–diffusion processes [1,2]. Classical finite difference methods are not reliable to preserve the stability property as they require the introduction of very fine meshes inside the boundary layers, which requires more computational cost They could not capture the solutions in the layer region of the domain as the solution. The purpose of the study is to develop a convergent and more accurate spline method for solving third-order singularly perturbed boundary value problem and that works for the cases where other numerical methods fail to give good results. This method depends on exponential spline function which has exponential and polynomial parts.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
