An Efficient Third-Derivative Hybrid Block Method for the Solution of Second-Order BVPs

Abstract

A new one-step hybrid block method with two-point third derivatives is developed to solve the second-order boundary value problems (BVPs). The mathematical derivation of the proposed method is based on the interpolation and collocation methods. The theoretical properties of the proposed method, such as consistency and convergence, are well analysed. Some BVPs with different boundary conditions are solved to demonstrate the efficiency and feasibility of the suggested method. The numerical results of the proposed method are much closer to the exact solutions and more competitive than other numerical methods in the available literature.

Keywords

• hybrid block method
• boundary value problems
• ordinary differential equations
• convergence analysis
• collocation and interpolation methods