A New Bernoulli Wavelet Method for Numerical Solutions of Nonlinear Weakly Singular Volterra Integro-Differential Equations-Reference-Cited by-同舟云学术

A New Bernoulli Wavelet Method for Numerical Solutions of Nonlinear Weakly Singular Volterra Integro-Differential Equations

Published:2017-04-13 Issue:03 Volume:14 Page:1750022
ISSN:0219-8762
Container-title:International Journal of Computational Methods
language:en
Short-container-title:Int. J. Comput. Methods

Author:

Sahu P. K.¹,Saha Ray S.¹

Affiliation:

1. Department of Mathematics, National Institute of Technology, Rourkela-769008, Odisha, India

Abstract

In this paper, Bernoulli wavelet method has been developed to solve nonlinear weakly singular Volterra integro-differential equations. Bernoulli wavelets are generated by dilation and translation of Bernoulli polynomials. The properties of Bernoulli wavelets and Bernoulli polynomials are first presented. The present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by Newton’s method. Convergence analysis of the present method has been discussed in this paper. Some illustrative examples have been demonstrated to show the applicability and accuracy of the present method.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computational Mathematics,Computer Science (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219876217500220

Reference17 articles.

1. Wavelet Interpolation Method for Solving Singular Integral Equations

2. Wavelets method for solving systems of nonlinear singular fractional Volterra integro-differential equations

3. Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations

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