This thesis presents a non-classical sinc method designed to address singular problems across various fields of science and engineering. The key innovation is the use of new non-classical weight functions instead of traditional ones in the sinc method. The approach achieves higher accuracy than conventional sinc-based numerical methods by choosing appropriate weight functions. It also addresses the non-differentiability issue of sinc basis functions at boundaries. We apply the non-classical sinc-collocation method to solve singular problems such as singularly perturbed two-point boundary value problems, singular third-order boundary value problems, nonlinear differential equations like the Lane-Emden equation, and integral equations such as Hallen’s and Pocklington’s. While the sinc method features exponential convergence, the non-classical sinc method, with the correct weight function, demonstrates even better exponential convergence. Numerical results show that our method provides good accuracy and efficiency compared to other methods with exponential convergence. We further analyze the convergence and provide error estimates for most of the sections
