Piecewise reproducing kernel method for singularly perturbed delay initial value problems

A direct application of the reproducing kernel method presented in the previous works cannot yield accurate approximate solutions for singularly perturbed delay differential equations. In this letter, we construct a new numerical method called piecewise reproducing kernel method for singularly perturbed delay initial value problems. Numerical results show that the present method does not share the drawback of standard reproducing kernel method and is an effective method for the considered singularly perturbed delay initial value problems.