An adaptive one-point second-derivative Lobatto-type hybrid method for solving efficiently differential systems

Abstract

This manuscript presents a one-step method incorporating a second-derivative applied to obtain approximate solutions of first-order initial-value problems of ordinary and time-dependent partial differential equations. The new scheme is derived through interpolation and collocation approaches, and the characteristics of the obtained method are analyzed. An embedding-like technique is considered and executed in adaptive mode to get better performance of the proposed method. The new scheme is used for solving some real-life application problems to determine its efficiency and accuracy. The numerical solutions obtained show that the proposed error estimate strategy is suitable in a variable step-size mode, robust and competitive compared with the results provided by other methods in the available literature.

KEYWORDS:

• Linear and non-linear IVPs
• ordinary and time-dependent partial differential equations
• hybrid block method
• variable step-size formulation
• stability analysis

2010 AMS SUBJECT CLASSIFICATIONS:

• 65L05
• 65L20

Disclosure statement

No potential conflict of interest was reported by the author(s).