A Bernoulli-reproducing kernel method for a class of nonlinear singular boundary value problems

Abstract

We have developed a highly accurate numerical method called Bernoulli-RKM to solve nonlinear singular boundary value problems (SBVPs). This approach uses Bernoulli polynomials and the traditional reproducing kernel method (RKM) and applies the quasi-linearization method to linearize the SBVPs. We have discussed the error and convergence of Bernoulli-RKM and provided numerical examples to demonstrate its potential in solving nonlinear SBVPs. Additionally, we have compared our results with those in existing literature.