A New Hybrid Block Method for Solving First-Order Differential System Models in Applied Sciences and Engineering

Abstract

This paper presents a new hybrid block method formulated in variable stepsize mode to solve some first-order initial value problems of ODEs and time-dependent partial differential equations in applied sciences and engineering. The proposed method is implemented considering an adaptive stepsize strategy to maintain the estimated error in each step within a specified tolerance. In order to evaluate the performance and usefulness of the proposed technique in real-world applications, several differential problems from applied sciences and engineering, such as the SIR model, Jacobi elliptic function problem, and chemical reactions problems, are solved numerically. The results of numerical simulations in this work demonstrate that the proposed method is more efficient than other existing numerical methods used for comparisons.

Keywords

• hybrid block method
• variable stepsize formulation
• initial value problems
• ordinary differential equations
• time-dependent partial differential equations