Septic B-spline Technique for Numerical Treatment of Singularly Perturbed Boundary Value Problems

Abstract

In this communication, Septic B-spline technique is introduced for numerical treatment of linear
and nonlinear second order singularly perturbed boundary value problems (SPBVPs). Non-linear problems
are linearized with the help of quasilinearization techniques and Septic B-spline technique is directly
implemented to the linear second order SPBVPs. Convergence analysis of the proposed technique is also
proved and found that it gives six order convergence results. The numerical results exhibit that present
technique gives more accurate numerical solutions as compared to other existing methods.