A new decomposition method - the “Upadhyaya decomposition method” - for the solution of the linear Volterra integro-differential equations of the second kind

Abstract

This study introduces a new decomposition method called the “Upadhyaya decomposition method” for solving the problem of linear Volterra integro-differential equations of the second kind. This method is the combination of the Upadhyaya transform and the decomposition method. Three numerical problems provide a detailed description and illustration of the procedure. According to the results the current approach is quite effective and it provides the answers without requiring laborious computational efforts.