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In this study, a singularly perturbed convection-dominated diffusion equation is solved by using a non-polynomial spline method. An example is solved to assess the accuracy of the method. The numerical results are obtained for different perturbed values ($\epsilon$ ) of equation. The results indicate that non-polynomial spline method is effectively implemented. It is seen that results are compatible with exact solutions and consistent with other existing numerical methods.

In this paper, we have discussed a third-degree non-polynomial spline solution for the numerical solution to nonlinear boundary value problems (BVPs) and compare other metods. Two numerical examples are given to illustrate the efficiency and performance of the method. The method gives accurate results in both the linear and nonlinear cases.