Derivation Error Formulas for the SySy Technique and a Study of its Efficiency in Calculating Double Integrals Improper and Improper Derivatives Numerically

Abstract

The primary objective of this study is to derive a general formula for the correction 

terms associated with the proposed method, particularly in cases where the 

integrand is continuous while its derivatives are improper, or when the integrand 

exhibits impropriety at one or more points within the domain of integration.

This study presents several theorems aimed at determining error expressions for such 

types of double integrals, whether the impropriety arises at the lower bounds, upper 

bounds, or both simultaneously. Five illustrative examples are provided to demonstrate 

various cases of double integrals, and supplementary tables are included to present 

detailed results