Discrete singular convolution mapping methods for solving singular boundary value and boundary layer problems

A modified discrete singular convolution method is proposed. The method is based on the single (SE) and double (DE) exponential transformation to speed up the convergence of the existing methods. Numerical computations are performed on a wide variety of singular boundary value and singular perturbed problems in one and two dimensions. The obtained results from discrete singular convolution methods based on single and double exponential transformations are compared with each other, and with the existing methods too. Numerical results confirm that these methods are considerably efficient and accurate in solving singular and regular problems. Moreover, the method can be applied to a wide class of nonlinear partial differential equations.