An adaptive mesh hybrid block method for solving nonlinear singularly perturbed differential equations

In this paper, we present an efficient numerical method for first order nonlinear singularly perturbed differential equations. This method is based on a hybrid block method with four hybrid points on a non-uniform mesh. The main characteristics of the hybrid block method, including consistency, zero stability and stability region are investigated. In order to optimize mesh points, we will use the interpolation technique and arc-length monitor function. After finding the new optimized mesh points, we can apply the proposed hybrid block method to optimize the numerical solution. The numerical experiments show the efficiency and accuracy of the proposed method.