An approximate solution method of Abel’s integral equation in the Hilbert space
Annotatsiya
Many problems in mechanics and mathematical physics are reduced to solving integral equations. Developing optimal approximate methods for solving such integral equations in functional spaces is one of the urgent problems of computational mathematics. In this paper, the solution of integral equations of fractional order, in particular, the analytical solution of the general Abel integral equation, is presented. It is devoted to constructing an optimal quadrature formula for approximating a general Abel integral equation in the Hilbert space real-valued functions. Here, we find the extremal function and calculate the square of the error functional norm for the quadrature formula. We also calculate the optimal coefficients for the quadrature formulas. The optimal quadrature formula is constructed by finding the optimal coefficients that give minimum to the norm of the error functional.