Solving nonlinear mixed Volterra–Fredholm integral equations with two dimensional block-pulse functions using direct method

✍ Scribed by K. Maleknejad; K. Mahdiani

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 265 KB
• Volume: 16
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2010.12.036

✦ Synopsis

a b s t r a c t

Few numerical methods such as projection methods, time collocation method, trapezoidal Nystrom method, Adomian decomposition method and some else are used for mixed Volterra-Fredholm integral equations. The main purpose of this paper is to use the piecewise constant two-dimensional block-pulse functions (2D-BPFs) and their operational matrices for solving mixed nonlinear Volterra-Fredholm integral equations of the first kind (VFIE). This method leads to a linear system of equations by expanding unknown function as 2D-BPFs with unknown coefficients. The properties of 2D-BPFs are then utilized to evaluate the unknown coefficients. The error analysis and rate of convergence are given. Finally, some numerical examples show the implementation and accuracy of this method.