The numerical solution of inverse nodal problem for integro-differential operator by Legendre wavelet method

Abstract

In this study, integro-differential equation under separated boundary conditions is considered. In fact, we study the inverse nodal problem, which includes differential part of Sturm–Liouville equation and Volterra type integral to obtain approximative solutions by Legendre polynomials. And, we use Legendre wavelets method to solve these types of problems. In addition, we present the error bound of $q(x)$ for continuous derivatives with its approximative solution. Once and for all, the strength of the method can be seen in a few examples.

Keywords:

• Integro-differential operator
• inverse nodal problem
• approximative solution
• Legendre wavelet method

2010 AMS SUBJECT CLASSIFICATIONS:

• 34A55
• 34B99

Disclosure statement

No potential conflict of interest was reported by the author(s).