New generalized operational matrix of integration to solve nonlinear singular boundary value problems using Hermite wavelets

Abstract

In this article, we developed new operational matrix of integration using Hermite wavelets and represented in generalized form also contributed a new algorithm (Hermite wavelets operational matrix method) for obtaining solutions of second-order nonlinear singular boundary value problems. The properties of Hermite wavelets are used to convert the problems into system of algebraic equations which can be efficiently solved by suitable solvers. Illustrative numerical examples are considered to demonstrate the applicability of this technique and those results are comparing favourably with the exact solutions. Also we have discussed some properties of Hermite wavelets and theorems on Hermite space.

Keywords

• hermite wavelets
• nonlinear singular boundary value problems
• collocation method
• operational matrix of integration
• banach space