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Solving nonlinear mixed Volterra-Fredholm integral equations with two dimensional block-pulse functions using direct method. (English) Zbl 1222.65149
Summary: 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 (VFIEs) of the first kind. This method leads to a system of linear equations by expanding unknown functions 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.
##### MSC:
 65R20 Integral equations (numerical methods) 45B05 Fredholm integral equations 45D05 Volterra integral equations 45G10 Nonsingular nonlinear integral equations
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