Solve Partial Differential Equations using the Banach Contraction Method and Improve Results Using the Trapezoidal Rule

Abstract

In this paper, the Banach contraction method (BCM) was hybridized with the base of the trapezoid (TR) to solve non-linear partial differential equations. The results obtained from (BCM) were improved by (TR). The results obtained from (BCM -TR) proved the efficiency of this method compared to the default method (BCM). This was done by calculating the mean0square0error (MSE) and estimating the absolute0maximum0error (MAE).

Keywords

• banach contraction method
• trapezoidal rule
• partial differential equations