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Hybrid Bernstein block-pulse functions method for second kind integral equations with convergence analysis. (English) Zbl 1474.65487

Summary: We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval \([0, 1]\). These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

MSC:

65R20 Numerical methods for integral equations
45L05 Theoretical approximation of solutions to integral equations
45B05 Fredholm integral equations
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