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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.
65R20Integral equations (numerical methods)
45B05Fredholm integral equations
45D05Volterra integral equations
45G10Nonsingular nonlinear integral equations
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