Abstract
In the current paper, an efficient numerical method based on two-dimensional hybrid of block-pulse functions and Legendre polynomials is developed to approximate the solutions of two-dimensional nonlinear Fredholm, Volterra and Volterra–Fredholm integral equations of the second kind. The main idea of the presented method is based upon some of the important benefits of the hybrid functions such as high accuracy, wide applicability and adjustability of the orders of block-pulse functions and Legendre polynomials to achieve highly accurate numerical solutions. By using the numerical integration and collocation method, two-dimensional nonlinear integral equations are reduced to a system of nonlinear algebraic equations. The focus of this paper is to obtain an error estimate and to show the convergence analysis for the numerical approach under the L2-norm. Numerical results are presented and compared with the results from other existing methods to illustrate the efficiency and accuracy of the proposed method.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
