Three-step Collocation Method for Solution of Third Derivative Initial Value Problem

Abstract

In this research paper, we introduce a novel three-step block method designed to directly tackle third-order initial value problems. This method is crafted through an interpolation and collocation approach, leveraging power series analysis. We conduct a comprehensive examination of the proposed method, ensuring it meets all requisite conditions for rigorous analysis. To assess its efficacy and validity, we employ the method on both highly stiff linear and nonlinear initial value problems, juxtaposing our findings with established approaches in the literature. Our results highlight that the new method exhibits faster convergence compared to existing methods, underscoring its superior performance. Initial value problems, Interpolation and collocation procedure, Three step, Third order