Improved the results of the Banach contraction method using the trapezoidal rule for solving differential equations

Abstract

In this work, the Banach contraction method (BCM) was hybridized with the trapezoidal rule (TR) to solve linear and nonlinear ordinary differential. The results obtained from Banach contraction method using the trapezoidal rule were improved by solving some examples and the results showed that the proposed method is better than the default method, where the maximum absolute error (MAE) was calculated, as well as the mean square error (MSE) of the default and proposed method, and the results of the two methods were also drawn by using Maple program.

Subject Classification:

• 34G10
• 34G20
• 97N40
• 46N40

Keywords:

• Banach contraction method
• Trapezoidal rule
• Linear and nonlinear differentiation equations