New Algorithms for Numerical Assessment of Nonlinear Integro-Differential Equations of Second-Order using Haar Wavelets

Abstract

This paper deals with the extended design for Fredholm and Volterra integral equations and design for Fredholm and Volterra integro-differential equations of first-order to second-order nonlinear Fredholm and second-order nonlinear Volterra integro-differential equations having square integrable kernels. This approach utilizes the inherent dynamics of the Haar wavelet. The Haar wavelet is used to provide a single platform for the proposed method. The method is tested on problems from literature, and numerical results are compared with existing methods. The numerical results indicate that the accuracy of the method is reasonably high, even on a coarse grid. doi:10.14456/WJST.2015.39

Keywords

• Haar wavelet
• collocation method
• second-order Fredholm integro-differential equation of second kind
• second-order Volterra integro-differential equations of second kind