The Discrete Galerkin Method for Nonlinear Integral Equations
نویسنده
چکیده
Let K be a completely continuous nonlinear integral operator, and consider solving x = K(x) by Galerkin's method. This can be written as xn = PnK(xn),Pn an orthogonal projection; the iterated Galerkin solution is defined by xn = K(xn). We give a general framework and error analysis for the numerical method that results from replacing all integrals in Galerkin's method with numerical integrals. A special high order formula is given for integral equations arising from solving nonlinear two-point boundary value problems.
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